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 1. JSTOR Model Completeness Results For Expansions Of The Ordered On one hand, the failure of Quantifier elimination shows that the best that could be hoped for is model completeness that relative to the theory of thehttp://links.jstor.org/sici?sici=0022-4812(199906)64:2<910:MCRFEO>2.0.CO;2-W

2. Model Theory - Wikipedia, The Free Encyclopedia
One can see from the definition that Quantifier elimination is stronger than model completeness. This is because formulas in model complete theories are
http://en.wikipedia.org/wiki/Model_theory
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##### Model theory
This article discusses model theory as a mathematical discipline and not the term mathematical model which is used informally in other parts of mathematics and science.
In mathematics model theory is the study of (classes of) mathematical structures such as groups fields graphs or even models of set theory using tools from mathematical logic . Model theory has close ties to algebra and universal algebra This article focuses on finitary first order model theory of infinite structures. The model theoretic study of finite structures (for which see finite model theory ) diverges significantly from the study of infinite structures both in terms of the problems studied and the techniques used. Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness does not in general hold for these logics. However, a great deal of study has also been done in such languages.
##### Contents

3. Seminars In Pure Mathematics | Logic Seminar
Abstract, model completeness is one of the main methods for proving that For example, Macintyre s Quantifier elimination provided the foundation for
http://www.math.uwaterloo.ca/PM_Dept/Research/Seminars/logic.shtml
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##### Logic Seminars
Upcoming Logic Seminars Past Seminars Wednesday, November 28 , 2007 Speaker: Gareth Jones
McMaster University Title: Model completeness and o-minimality. Abstract: Model completeness is one of the main methods for proving that structures are o-minimal. There are also some results showing that certain o-minimal structures are model complete. I'll present some of these results, and say why they are useful. Time: 2:30 p.m.

4. DC MetaData For:Non-effective Quantifier Elimination
03C10 Quantifier elimination, model completeness and related topics 03D80 Applications of computability and recursion theory. Abstract
 Non-effective quantifier elimination Source file as Postscript Document TeX DVI Data Mihai Prunescu Preprint series: Preprintreihe Mathematik 9/2000, MSC 2000 03C10 Quantifier elimination, model completeness and related topics 03D80 Applications of computability and recursion theory Abstract We study the general connections between quantifier elimination and decidability for first order theories.

 5. Baztech Informacja O Publikacji Tytul A modeltheoretic criterion for Quantifier elimination and its application and does not involve model-completeness or Robinson s test as does forhttp://baztech.icm.edu.pl/baztech/cgi-bin/btgetdoc.cgi?BAT2-0001-0940

6. Model Theory: An Introduction
Vaught s Test, completeness of algebraically closed fields, Ax s Theorem Quantifier elimination constructible sets model theoretic proof of the
http://www.math.uic.edu/~marker/mtcont.html
• ##### Chapter 1 : Structures and Theories
• Languages and Structures
• Theories
• Definable Sets and Interpretability
interpreting a field in the affine group, interpreting orders in graphs
• ##### Chapter 2: Basic Techniques
• The Compactness Theorem
• Complete Theories
Vaught's Test, completeness of algebraically closed fields, Ax's Theorem
• Up and Down
elementary embeddings, Lowenheim-Skolem
• Back and Forth
dense linear orders, the random graph, Ehrenfeucht-Fraisse Games, Scott sentences
• ##### Chapter 3: Algebraic Examples
• Quantifier Elimination
quantifier elimination test, qe for torsion free divisible abelian groups groups, qe for divisible ordered abelian groups, qe for Pressburger arithmetic
• Algebraically Closed Fields
• Real Closed Fields
• ##### Chapter 4: Realizing and Omitting Types
• Types
Stone spaces, types in dense linear orders and algebraiclly closed fields
• Omitting Types and Prime Models
Omitting types theorem, prime and atomic models, existence of prime model extensions for omega-stable theories
• Saturated and Homogeneous Models
• The Number of Countable Models
aleph_0-categorical theories, Morley's theorem on the number of countable models

 7. A (restricted) Quantifier Elimination For Security Protocols This leads to a Quantifier elimination result for the logic which establishes the . 25 25 G. Lowe, Towards a completeness result for model checking ofhttp://portal.acm.org/citation.cfm?id=1226654

 8. CiE 2006 - Regular Talk: - Basic Model Theory For Bounded Theories Notions like Quantifier elimination or model completeness are also well studied in model theory. We define similar notions and prove similar theorems forhttp://www.cs.swan.ac.uk/cie06/giveabs.php?216

9. Education, Master Class 1988/1999, MRI Nijmegen
Contents model theory studies the variety of mathematical structures that by Quantifier elimination and Robinson s notion of model completeness.
http://www.math.uu.nl/mri/education/course_9899.html
 Education, Master Class, Master Class 1998/1999, Detailed Course Content Detailed Content of the Courses Course content 1st semester: Model Theory W. Veldman Lambda Calculus H. Barendregt, E. Barendsen Recursion Theory and Proof Theory H. Schellinx Logic Panorama seminar 2nd semester: Type Theory and Applications H. Barendregt, E. Barendsen Incompleteness Theorems J. van Oosten Sheaves and Logics I. Moerdijk Mathematical Logic seminar Courses Name of the course: Model Theory Lecturer: W. Veldman Prerequisites: Some familiarity with mathematical reasoning. Literature: C.C. Chang, H.J. Keisler, Model Theory, North Holland Publ. Co. 1977 W. Hodges, Model Theory, Cambridge UP, 1993 Contents: Model theory studies the variety of mathematical structures that satisfy given formal theory. It may also be described as a study of mathematical structures from the logician's point of view. Model theory at its best is a delightful blend of abstract and concrete reasoning. Among the topics to be treated in this course are Fraisse's characterisation of the notion 'elementary equivalence' (structures A,B are called elementarily equivalent if they satisfy the same first-order-sentences), the compactness theorem and its many consequences, ultraproducts, some non-standard-analysis, Tarski's decision method for the field of real numbers by quantifier elimination and Robinson's notion of model completeness. If time permits, some attention will be given to constructive and recursive model theory.

10. MODNET Summer School, Leeds, Dec. 12 - 17, 2005
Brief synopsis (topics from the following list) brief summary of the prerequisites below, Quantifier elimination, model completeness, model completions and
http://www.maths.leeds.ac.uk/pure/logic/modnet.dec.html
##### MODNET Summer School, University of Leeds, December 12 - 17, 2005
This event will consist of three short courses, each of around 5 - 6 lectures, supported by tutorials in the evenings. It is the first training event of the Marie Curie Framework 6 Research Training Network MODNET , funded by the European Commission. It is intended for PhD students at an early stage of their doctorate (e.g. first or second year), but we welcome participation by others, e.g. MSc students, or by other researchers, possible more experienced, for whom model theory is a peripheral interest. Lecture Courses:
• Intermediate Model Theory (5 lectures. Lecturer: Mike Prest, University of Manchester) Brief synopsis (topics from the following list): brief summary of the prerequisites below, quantifier elimination, model completeness, model completions and companions, the topology on the Stone space of types and Cantor-Bendixson rank, prime models and the monster model, elimination of imaginaries, indiscernibles and Skolem functions, FraissÃ© constructions, omega-categoricity. Prerequisites (intended as guidelines of helpful background the more advanced topics below will not be essential to understand the course): completeness and compactness for first order logic; LÃ¶wenheim-Skolem theorems, ultraproducts, elementary extensions and chains, types, saturation, omitting types and Ryll-Nardzewski, countable atomic and prime models.
• 11. Logic And Computation
Categoricty and the o Vaught Test; Substructures and Elementary Substructures; model completeness and the Robinson Test; Quantifier Elimination
http://cca-net.de/vasco/lc/
Module 3LC for third year mathematics MAM3.
##### Lecturer
Vasco Brattka
University of Cape Town
##### Time Table (2007)
The lectures take place in at (fourth period) on Tuesdays Fridays and the following Wednesdays
• 28 Feb, 14 Mar, 18 Apr, 25 Apr, 2 May, 16 May.
The tutorial takes place in ZOO 3 at (sixth period), each Tuesday
##### Course Description
In particular, we will cover the following topics:
• distinction between syntax and semantics,
• propositional logic,
• first-order logic,
• theories and models,
• arithmetic.

www.mcescher.com
##### Part A: Propositional Logic
• Introduction
• Introduction
• Historical Background
• Aristotle's Analytics
• Hilbert's Program
• Syntax and Semantics
• Different Logics
• Syntax of Propositional Logic
• Propositional Logic
• Symbols of Propositional Logic
• Syntax of Propositional Logic
• Formation Trees
• Recursive Definitions and Structural Induction
• Semantics of Propositional Logic
• Semantics of Propositional Logic
• Truth Tables
• Evaluation of Formulas with Trees
• Satisfiability and Tautologies
• Coincidence Lemma
• The Truth Table Method
• Logical Implication and Equivalence
• Logical Implication and Equivalence
• Syntactical Implications and Logical Consequences
• Realizability of Boolean Functions
• Disjunctive and Conjunctive Normal Form
• Complete Sets of Connectives
• Digital Circuits
• The Compactness Theorem
• Satisfiability and Logical Consequences of Sets of Formulas
• The Compactness Theorem
• Computability Notions for Subsets
• Notions of Computability
• Computability and Computable Enumerability
• The Truth Table Method
• 12. Trimester On Real Geometry - Abstracts
modelcompleteness results will be proved for each individual case, . Uniform (Local) Quantifier Elimination and its application in constraint databases.
http://perso.univ-rennes1.fr/michel.coste/Borel/realgeomabs.html
##### Abstracts of the courses
Back to the programme
• F. Acquistapace (September 14th - October 1 3th, 8 lectures): Around Hilbert's 17th problem for analytic functions
In this course we will study several properties of the ring of analytic functions on a real analytic manifold . We will also study important properties of the sets which are defined using the ring of analytic functions on
We will discuss several problems for those global functions and sets, which are classical for semialgebraic sets and regular functions, namely:
Hilbert Problem: Let for any . Is a sum of squares of meromorphic functions? Nullstellensatz: Given an ideal , how can we caracterize the ideal Positivstellensatz: Given , how can we caracterize the set of functions which are on the set Closure: Is the closure of a global analytic set still a global semianalytic set? Connected components: Is a union of connected components of a global semianalytic set still a global semianalytic set? Finiteness: Let be a global open (resp.

13. 6th Panhellenic Logic Symposium :: Programme
While keeping modelcompleteness and Quantifier-elimination as the main conceptual tools, we traverse in a uniform way various applications domains,
http://pls6.pre.uth.gr/programme.php
##### Programme
Thursday 5.7.07
Registration - Opening
Constantine Tsinakis (Vanderbilt University):
Algebraic Methods in Logic Algebraic logic studies classes of algebras that are related to logical systems, as well as the process by which a class of algebras becomes the algebraic counterpart (semantics)" of a logical system. A field practitioner usually approaches the solution of a problem in logic by first reformulating it in the language of algebra; then by using algebra to solve the reformulated problem; and lastly by expressing the result into the language of logic. A representative association of the preceding kind is the one between the class of Boolean algebras and classical propositional calculus.
The focus of this talk is substructural logics and their algebraic counterparts. Substructural logics are non-classical logics that are weaker than classical logic, in the sense that they lack one or more of the structural rules of contraction, weakening and exchange in their Genzen-style axiomatization. (It is, however, convenient to think of the classical logic and intuitionistic logic as substructural logics.) These logics encompass a large number of non-classical logics related to computer science (linear logic), linguistics (Lambek Calculus), philosophy (relevant logics), and multi-valued reasoning.
The following are among the objectives of the talk:
Propose a uniform framework for the study of the algebraic counter-parts of substructural propositional logics. These algebras, referred to as residuated lattices, have a recently discovered rich structure theory. (Note: The term "residuated lattice" has been used in the literature to refer to algebras that are integral, commutative and bounded. This class and its subclasses are not sufficiently general to provide semantics for all substructural logics.)

14. 03Cxx
03C10, Quantifier elimination, model completeness and related topics. 03C13, Finite structures See also 68Q15, 68Q19. 03C15, Denumerable structures
http://www.impan.gov.pl/MSC2000/03Cxx.html

 15. CSL/KGC'03 - Nicolai Vorobjov: Effective Model Completeness Of The Theory Of Res Nicolai Vorobjov Effective model completeness of the theory of restricted by restricted Pfaffian functions does not admit Quantifier elimination.http://www.logic.at/csl03/giveabs.php?156

 16. HeiDOK 03C10 Quantifier elimination, model completeness and related topics ( 0 Dok. ) 03C13 Finite structures ( 0 Dok. ) 03C15 Denumerable structures ( 0 Dok.http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03C&anzahl

17. Infinity Symposium - The Infinity Project
In this talk, we explore a new road via abstract model theory, topics such as model completeness and (standard, first order) Quantifier elimination.
http://fspc282.few.vu.nl/infinity/index.php/Infinity_Symposium
##### From The Infinity Project
A past event: the spring symposium for our BRICKS project INFINITY
INFINITY SYMPOSIUM Tuesday March 21 and Wednesday March 22, 2006 Room S111, Faculty of Sciences, Vrije Universiteit Amsterdam
The project is concerned with infinite objects, computation, modeling, and reasoning (more information can be found here ). For participants of the INFINITY project, the symposium is meant as an opportunity to learn about related work and meet people working in related fields. Most talks will be of a tutorial nature. The symposium takes place in between two PhD defenses (see Past events ) that both have to do with the subject of INFINITY
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##### Wednesday March 22, 2006

18. 17. CSL 2003: Vienna, Austria
Effective model completeness of the Theory of Restricted Pfaffian Functions Effective Quantifier Elimination over Real Closed Fields (Tutorial). 545
http://www.informatik.uni-trier.de/~ley/db/conf/csl/csl2003.html
##### CSL 2003: Vienna, Austria
Matthias Baaz Johann A. Makowsky Lecture Notes in Computer Science 2803 Springer 2003, ISBN 3-540-40801-0 BibTeX DBLP

19. A Shorter Model Theory (Paperback) Is Available From Bestprices.com Books!
A Shorter model Theory only \$48.99, get the A Shorter model Theory book From the SkolemTarski method of Quantifier elimination, model completeness,

20. Oxford Mathematical Logic Group - Seminars - Junior Logic Seminar
Week 7, Philipp Hieronymi, modelcompleteness for some discrete, o-minimal, 22nd November, Philipp Hieronymi, Analytic Quantifier elimination for Zp
http://www2.maths.ox.ac.uk/logic/juniorseminars.shtml
##### Oxford Mathematical Logic Group
Mathematical Institute University of Oxford
##### Hilary term 2007
Week 1 Tom Foster Compactness in o-minimal structures Week 2 Christian Reiher Set Theory and the Two Cardinal Assertion Week 3-7 The Mordell-Lang conjecture
##### Michaelmas term 2006
Week 1 No seminar Week 2 David Bew Towards definining C-infinity Week 3 No seminar Week 4 Margaret Thomas Siegel's Three Primes Theorem Week 5 Juan Diego Caycedo A free amalgamation construction Week 6 David Bew Fusing o-minimal structures Week 7 Philipp Hieronymi Model-completeness for some discrete, o-minimal, green fields Week 8 Martin Bays Groupoid actions, internality and differential Galois theory
##### Trinity term 2006
1st May Martin Bays The geometry of a non-trivial modular minimal type II 8th May Gareth Jones 15th May Juan Diego Caycedo Bicoloured fields on the complex numbers 22th May Philipp Hieronymi The valuation property for power-bounded theories 29th May David Bew A division algorithm of Grauert and Hironaka 5th June Margaret Thomas O-minimal reparametrisation 12th June Jamshid Derakhshan Denef's rationality theorem on local integrals and related topics
##### Hilary term 2006
17th January David Bew Euler characteristics and pigeonhole principles 31st January Philipp Hieronymi The Wilkie inequality and the valuation property for T an 7th February Margaret Thomas Quasianalytic Denjoy-Carleman classes 14th February Martin Bays The geometry of a non-trivial modular minimal type 21st February Juan Diego Caycedo Getting a field in a Desarguesian projective plane

21. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
model classes axiomatic 08C10 model completeness and related topics Quantifier elimination, 03C10 model constructions other 03C30
http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_36.htm
 mechanics and problems of quantization # general quantum mechanics of deformable solids 74-XX mechanics of particles and systems 70-XX mechanics of solids # generalities, axiomatics, foundations of continuum mechanics type models; percolation theory # interacting random processes; statistical mechanics with other effects # coupling of solid mechanics, general relativity, laser physics) # dynamical systems in other branches of physics (quantum mechanics, regularization # collisions in celestial mechanics, structure of matter # statistical 82-XX mechanics; quantum logic # logical foundations of quantum mechanisms, robots mechanization of proofs and logical operations media and their use in instruction # audiovisual media with periodic structure # homogenization; partial differential equations in media, disordered materials (including liquid crystals and spin glasses) # random media. educational technology # educational material and media; filtration; seepage # flows in porous medical applications (general) medical epidemiology medical sciences # applications to biology and medical topics # physiological, cellular and

22. A SHORTER MODEL THEORY. - HODGES, WILFRID,
Pb. An upto-date textbook of model theory taking the reader from first the Skolem-Tarski method of Quantifier elimination, model completeness,
http://www.antiqbook.nl/boox/avv/22188.shtml
 ANTI Q BOOK Search Antiqbook Ask a question or Order this book Browse our books ... Book dealer info HODGES, WILFRID, A SHORTER MODEL THEORY. Cambridge, University Press, 1997. 1e edition 310 pages. Pb. An up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting tiypes theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, 0-minimality and structures of finite Morley rank.Some highlighted marks in the text. good condition EUR 12.50 = appr. US\$ 18.3125 Offered by: Antiquariaat Van Veen - Book number: 22188 Hundreds of the world's finest antiquarian and used booksellers offer their books on Antiqbook. They offer full satisfaction and normal prices - no markups, no hidden costs, no overcharged shipping costs. 7 million books at your fingertips! Search all books at Antiqbook

23. Volker Weispfenning
modelcompleteness and elimination of quantifiers for subdirect products of structures, Journal of Algebra 36 (1975), pp. 252-277.
http://staff.fim.uni-passau.de/algebra/staff/w-pub.php3
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##### Publications
• Elementary theories of valued fields
• Infinitary model theoretic properties of kappa-saturated structures , Zeitschrift Mathematische Logik und Grundlagen der Mathematik 19 (1973), pp. 97-109.
• , Trans. AMS 203 (1975), pp. 331-342.
• Commutative regular rings without prime model extensions (with D. Saracino), Proceeding AMS 47 (1975), pp. 201-207.
• Model-completeness and elimination of quantifiers for subdirect products of structures , Journal of Algebra 36 (1975), pp. 252-277.
• 24. Springer Online Reference Works
The model completeness was applied to valued function fields (cf. Valued function field). The elimination of quantifiers was applied in the early 1990s by
http://eom.springer.de/M/m110170.htm

Encyclopaedia of Mathematics
M
Article referred from
Article refers to
Model theory of valued fields
A branch of model theory concerned with the elementary theories of fields with valuations (cf. Elementary theory Field Valuation ). The basic first-order language is that of rings (or fields) together with a unary relation symbol for being an element of the valuation ring, or a binary relation symbol for valuation divisibility (cf. Structure
##### Algebraically closed valued fields.
A. Robinson proved that the elementary theory of all algebraically closed valued fields is model complete . It can be deduced from his work that this theory is decidable and admits elimination of quantifiers . If, in addition, the characteristic of the fields and of their residue fields is fixed, then the theory so obtained is complete. The proof uses the fact that all extensions of a valuation of a field to its algebraic closure are conjugate, i.e., the algebraic closures of a valued field are isomorphic as valued fields. Robinson's results have witnessed many applications. The model completeness was applied to valued function fields (cf. Valued function field ). The elimination of quantifiers was applied in the early

25. Transactions Of The American Mathematical Society
We give an analytic Quantifier elimination theorem for (complete) algebraically applications of Quantifier elimination for valued fields, model Theory,
http://www.ams.org/tran/2005-357-11/S0002-9947-05-04003-1/home.html
 ISSN 1088-6850(e) ISSN 0002-9947(p) Previous issue Table of contents Next issue Articles in press ... Next Article Uniform properties of rigid subanalytic sets Author(s): Leonard Lipshitz; Zachary Robinson Journal: Trans. Amer. Math. Soc. MSC (2000): Primary 03C10, 32P05, 32B20; Secondary 26E30, 03C98 Posted: June 21, 2005 Retrieve article in: PDF DVI PostScript Abstract ... Additional information Abstract: In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quantifier elimination theorem for (complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quantifier elimination is independent of the valued field's characteristic, residue field and value group, in close analogy to the algebraic case. This provides uniformity results about rigid subanalytic sets. We obtain uniform versions of smooth stratification for subanalytic sets and the ojasiewicz inequalities, as well as a unfiorm description of the closure of a rigid semianalytic set.

26. Quantifier Elimination Vs Model Complete Theories
I have as a theorem in my notes the following The following are equivalent T is model complete T has Quantifier elimination Fot any model A of T,
http://www.archivum.info/sci.logic/2006-08/msg00261.html
sci.logic Top All Lists Date Enter your search terms Submit search form Web www.archivum.info Thread
##### Quantifier Elimination vs Model Complete Theories
from [ Blake Manner Subject Quantifier Elimination vs Model Complete Theories From "Blake Manner" < Date 8 Aug 2006 06:56:31 -0700 Newsgroups sci.logic I have as a theorem in my notes the following: The following are equivalent: T is model complete T has quantifier elimination Fot any model A of T, T unioned with the basic diagram of A is a complete theory of L(A). I was just talking to someone about this and was corrected that model complete does not imply quantifier elimination (although QE does imply MC). Can someone offer me any insight on this? More with this subject... Current Thread
• Quantifier Elimination vs Model Complete Theories Blake Manner
Previous by Date: Characterization of Gamma_0 Daryl McCullough Next by Date: Re: Question regarding infinite length integers Newberry Previous by Thread: Characterization of Gamma_0 Daryl McCullough Next by Thread: Enumerable sets herbzet Indexes: Date Thread Top All Lists

27. Quantifier Elimination Vs Model Complete Theories
Science Forum Index Â» Logic Forum Â» Quantifier Elimination vs model Complete Theories. Page 1 of 1. Author, Message. Blake Manner

28. FOM: New Model Theory Text
Springer has just published my book model Theory An Introduction, Closed Fields Quantifier elimination constructible sets model theoretic proof of
http://cs.nyu.edu/pipermail/fom/2002-August/005776.html
##### FOM: new Model Theory text
Dave Marker marker at math.uic.edu

29. A Model Complete Theory Of Valued D-Fields
A model Complete Theory of Valued DFields. Thomas Scanlon Quantifier elimination and a version of the Ax-Kochen-Ersov principle is proven for a theory
http://projecteuclid.org/handle/euclid.jsl/1183746262
• Home Browse Search ... next
##### A Model Complete Theory of Valued D-Fields
Thomas Scanlon Source: J. Symbolic Logic Volume 65, Issue 4 (2000), 1758-1784.
##### Abstract
The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the Ax-Kochen-Ersov principle is proven for a theory of valued D-fields of residual characteristic zero. Full-text: Remote access If you are a member of the ASL, log in to Euclid for access. Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR. Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183746262 JSTOR: links.jstor.org back to Table of Contents previous next
##### Journal of Symbolic Logic

30. Books
The generalities of Quantifier elimination; The natural numbers; Lines model complete theories; The amalgamation property; Submodel complete theories
http://www.cs.man.ac.uk/~hsimmons/BOOKS/books.html
##### Books
A Book is a longer document written as a set of notes in the form of a book, and most are intended for publication in some form or other. One of these, Derivation and Computation , has been published already, but I don't have that in electronic form. Some of these books are in good shape, but still need a little polishing. One is little more than a random set of notes.
Here is a description of the contents of these documents in approximately in reverse chronological order of writing, that is with the latest at the top and the earliest at the bottom. I give a link to each document where it is a fit state to be let loose.
If you think any of these documents are worth completing and releasing, let me know and I will see what I can do.
• An introduction to lambda calculi and arithmetic
These notes are used as part of the course LINK TO BE INSERTED and cover about 10 to 15 hours of material. There are four chapters
• The untyped lambda-calculus lambda0
The basic syntax The reduction mechanism Fixed point and other combinators Final remarks
Simulation of arithmetic in lambda0
The church numerals Simulation of functions Closure under primitive recursion Closure under unbounded search Final remarks
The simply typed lambda calculus lambda1
Types, terms, and reductions

31. SQEMA
Algorithmic correspondence and completeness in modal logic. Quantifier elimination for secondorder predicate logic, in Logic, Language and Reasoning
http://www.fmi.uni-sofia.bg/fmi/logic/sqema
 Home SQEMA 0.9.2.2 SQEMA 0.9.8 Samples ... Thesis SQEMA an algorithm for computing first-order correspondences in modal logic: an implementation Dimiter Georgiev, Tinko Tinchev and Dimiter Vakarelov Sofia University Here is another interesting example, that is supported in the newer versions of SQEMA, courtesy of Renate Schmidt: p) p)) On the other hand, we are interested in examples of first-order definable modal formulae on which SCAN or DLS succeeds but SQEMA fails. If anyone finds such examples, pease send them to the webmaster . A most important feature of SQEMA is that, as proved in [2] and [3], it only succeeds on canonical (d-persistent) formulae, i.e., whenever successful, it not only computes a local first-order correspondent of the input modal formula, but also proves its canonicity and therefore the canonical completeness of the modal logic axiomatized with that formula. This accoridingly extends to any finite set of modal formulae on which SQEMA suceeds. Thus, SQEMA can also be used as an automated prover of canonical model completeness of modal logics. An implementation in Java of SQEMA was given in [1]. It supports nominals in the input and in the output gives a nominal formula and its translation into a first-order formula. Some simplifications of the first-order formula are also implemented.

32. CiteULike: Quantifier Elimination For The Reals With A Predicate For The Powers
Quantifier elimination for the reals with a predicate for the powers of two He gave a modeltheoretic argument, which provides no apparent bounds on the
http://www.citeulike.org/group/12/article/908314
##### Groups
• Search groups Info Library Messages ... Import
##### Copy-and-Pasteable Citation
(19 Oct 2006) Citation format: Plain APA Chicago Elsevier Harvard MLA Nature Oxford Science Turabian Vancouver
##### Abstract
In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretic argument, which provides no apparent bounds on the complexity of a decision procedure. We provide a syntactic argument that yields a procedure that is primitive recursive, although not elementary. In particular, we show that it is possible to eliminate a single block of existential quantifiers in time \$2^0_O(n)\$, where \$n\$ is the length of the input formula and \$2_k^x\$ denotes \$k\$-fold iterated exponentiation.
##### BibTeX

33. Research Interests
All structures described above are model complete; but do they admit Quantifier elimination (say, after adding bounded division) or even a preparation
http://www.math.mcmaster.ca/~speisseg/research.html
My research lies in the general areas of model theory and real analytic geometry. (Here is one possible description of how this fits into the general math picture.) The notion of o-minimal expansion of the field of real numbers provides a suitable setting for studying generalizations of the theory of semialgebraic sets, and I try to find new explicit examples of such expansions and study their geometric and model-theoretic properties. Many of these expansions are generated by certain solutions of differential equations, and the hope is to obtain new geometric insights from the o-minimality of these structures.
##### Expanding the real field by large classes of functions
As a graduate student at the University of Illinois, I constructed two such examples in joint work with my supervisor Lou van den Dries. Both expand the structure of globally subanalytic sets and define the exponential function. Moreover, one of them (the expansion of the field of reals by certain multisummable series ) also defines the Gamma function on all positive real numbers, while the other (the expansion of the field of reals by all convergent generalized power series ) defines the Riemann zeta function on all real numbers greater than 1. Each of these two examples is generated by the functions, restricted to compact sets, belonging to a certain quasianalytic class satisfying closure properties similar to (but weaker than) the closure properties satisfied by the class of all real analytic functions. Their construction relies on a combination of a form of Weierstrass preparation and blowing-ups due to Jean-Claude Tougeron, used to (locally) resolve the zerosets of functions in the respective class.

34. Curriculum Vitae. A) General Data. Born In Bucharest-Romania, 3.03
Using the model theoretic concept of existential completeness,certain types of good . Relative elimination of quantifiers for Henselian valued fields,
http://www.imar.ro/~sbasarab/
 Curriculum vitae. A) General data. Born in Bucharest-Romania, 3.03.1940, graduate of the Faculty of Electronics of the Technical University of Bucharest in 1961 and of the Faculty of Mathematics of the University of Bucharest in 1969 with a diplom thesis devoted to the Galois Cohomology, having the late Prof.Ionel Bucur as superviser. In 1977 I defended the PhD thesis with the title "Arithmetic and model theory" at the Faculty of Mathematics of the University of Bucharest under the supervision of Acad. Octav Onicescu, who replaced Prof.Ionel Bucur after his premature death. During the period 1979-1982, with some intrerruptions, I activated as visiting professor at the Institute of Mathematics of the University of Heidelberg thanks to a two years fellowship granted by the Alexander von Humboldt Foundation. As a member of the research group of Algebra and Number Theory, I have been decisively influenced by the personality of my academic mentor Prof. Peter Roquette. In 1983 I obtained a four months fellowship to visit the Universities of Firenze and Camerino-Italy, but unfortunatelly I was prevented from honouring the invitation by the communist Romanian authorities. In 1993 I visited the Universities of Wales-Bangor, Queen Marry-London, and Oxford Mathematical Institute under a three months fellowship granted by the European Communities.

35. 18.575 Model Theory
Topics to be covered include the compactness theorem, Quantifier elimination, realizing and omitting types, saturated and homogeneous models, indiscernibles
http://www-math.mit.edu/~rosen/18.575/
##### 18.575: Model Theory (Spring 2007)
Meetings MW 3:00-4:30, 2-142 Instructor Eric Rosen Office Email rosen (at) math (dot) mit (dot) edu Office Hours Wed. 2-3, Thur. 11-12, and by appointment Syllabus The course will be designed to provide the necessary model-theoretic background to understand significant recent applications to, e.g., diophantine geometry and motivic integration, in the work of Hrushovski, Kazhdan, Scanlon, Cluckers, Denef, and Loeser. Text Model Theory: An Introduction , by David Marker (Springer GTM). The introduction is available here . More information, including the table of contents, can be found on amazon Recommended reading Some other good introductions to the subject include Model Theory and A Shorter Model Theory , both by Wilfrid Hodges, and A Course in Model Theory by Bruno Poizat. These will be put on reserve in the library. An elegant description of the subject, also by Hodges, can be found here Lecture schedule: (tentative) My aim for the semester is to prove Morley's famous categoricity theorem, which was really the starting point for contemporary model theory. Much of the material covered in chapters 2, 4, and 5 gets used in the proof of this theorem. The ideas, tools, and techniques developed in these chapters are also fundamental to all further developments in the subject. Along the way, we will also examine connections with other areas of mathematics, especially algebra. In particular, chapter 3 contains an extended discussion of the model theory of algebraically closed fields, with glimpses at basic ideas in algebraic geometry.

36. A Model Complete Theory Of Valued D-Fields
Cited by More Quantifier Elimination for the Relative Frobenius Scanlon (Correct) Similar documents (at the sentence level) 26.2% A model Complete
http://nsdl.org/resource/2200/20061012115334157T

37. First-order Model Theory (Stanford Encyclopedia Of Philosophy)
In Robinson s terminology, a firstorder theory is model-complete if every .. of real numbers (which he proved by the method of Quantifier elimination;
http://plato.stanford.edu/entries/modeltheory-fo/
Cite this entry Search the SEP Advanced Search Tools ...
##### First-order Model Theory
First published Sat Nov 10, 2001; substantive revision Tue May 17, 2005 First-order model theory, also known as classical model theory, is a branch of mathematics that deals with the relationships between descriptions in first-order languages and the structures that satisfy these descriptions. From one point of view, this is a vibrant area of mathematical research that brings logical methods (in particular the theory of definition) to bear on deep problems of classical mathematics. From another point of view, first-order model theory is the paradigm for the rest of model theory ; it is the area in which many of the broader ideas of model theory were first worked out.
##### 1. First-order languages and structures
A a ). Two exceptions are that variables are italic ( x y ) and that sequences of elements are written with lower case roman letters (a, b).

38. Publications, H. Jerome Keisler
Quantifier elimination for neocompact sets. J. Symbolic Logic, 63 (1998), pp. 14421472. 87. Randomizing a model. Advances in Math. 143 (1999), pp. 124-158.
http://www.math.wisc.edu/~keisler/papers.html
##### Publications, H. Jerome Keisler
1. Theory of models with generalized atomic formulas, J. Symbolic Logic 25 (1960), pp. 1-26. 2. Ultraproducts and elementary classes, Ph. D. Thesis, Univ. of California, Berkeley, 1961, 45 pages. 3. On some results of Jonsson and Tarski concerning free algebras, Math. Scand. 9 (1961), pp. 102-106. 4. Ultraproducts and elementary classes, Indag. Math. 23 (1961), pp. 477-495. 5. Some applications of the theory of models to set theory, Proc. Int. Cong. of Logic, Methodology, and Philosophy of Science, Stanford 1962, pp. 80-85. 6. Model theories with truth values in a uniform space (with C.C.Chang), Bull. Amer. Math. Soc. 68 (1962), pp. 107-109. 7. An improved prenex normal form (with C.C.Chang), J. Symbolic Logic 27 (1962), pp. 317-326. 8. Applications of ultraproducts of pairs of cardinals to the theory of models (with C.C.Chang), Pacific J. Math. 12 (1962), pp. 835-845. 9. Limit ultrapowers, Trans. Amer. Math. Soc. 107 (1963), pp. 382-408. 10. A complete first-order logic with infinitary predicates, Fund. Math. 52 (1963), pp. 177-203. 11. Good ideals in fields of sets, Annals of Math. 79 (1964), pp. 338-359.

Some articles on continuous firstorder logic and the model theory of metric logic is complete and stable, and it admits Quantifier elimination when the
http://www.math.uiuc.edu/~henson/
 C. Ward Henson Professor, Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street, Urbana, Illinois 61801-2975 USA. email: henson(at)math(dot)uiuc(dot)edu Office: Room 310 Altgeld Hall ; (217) 333-2768; Fax: (217) 333-9576. Office hours (Fall, 2007): Mon. 4:00; Tues. 3:00; Fri. 3:00, and by appointment. Spring 2008 teaching (prospective): Math 571 (G1); MWF 3:003:50 in 443 Altgeld; Model Theory. The basic graduate course on model theory. Course advertisement Fall 2007 teaching: Math 424 (X1); MWF 12:0012:50 in 345 Altgeld; Honors Real Analysis A rigorous treatment of basic real analysis via metric spaces. Metric space topics include continuity, compactness, completeness, connectedness and uniform convergence. Analysis topics include the theory of differentiation, Riemann-Darboux integration, sequences and series of functions, and interchange of limiting operations. As part of the Mathematics Honors Sequence , this course will be rigorous and abstract. Enrollment needs department approval Course information . (gives textbook and syllabus, grading policies, dates of exams, etc.)

40. 22c:295 Seminar In Artificial Intelligence
Proof of soundness and completeness. TinSho. 03/24, Quantifier elimination in first order theories. Uses of QE. Obtaining decision procedures for full
http://www.cs.uiowa.edu/~tinelli/classes/295/logs.shtml
##### Spring 2005
Course Info Announcements Staff and Hours Syllabus Course Work Class Logs Projects Resources Readings Learning Research
##### Class Logs and Required Readings
The cited references can be found in the Readings section. Date Topics Readings Course introduction and motivation.
Introduction to propositional logic. Satisfiability and related notions: validity and entailment. Decidability of propositional satisfiability.
- [Por01] (suggested) Introduction to first-order logic. Syntax and semantics. More on first-order logic. Satisfiability and related notions: validity and entailment. Basic notions of computability and decidability. Undecidability of validity/satisfiability in first order logic.
Theories. validity/satisfiability modulo theories. First order logic with equality vs. first order logic withour equality. Embeddings of models and preservation properties. Normal models. Proof that the class of normal models is not elementary. The axioms of equality: the first order theory of equality. Example of a non-normal model for this theory. Reducibilty of the validity/satisfiability problem in normal models to the validity/satisfiability problem in models of the theory of equality.

41. Bounded Model Checking And Induction: From Refutation To Verification
This strengthening step requires Quantifierelimination, and we propose a lazy The effectiveness of induction based on bounded model checking and
http://www.csl.sri.com/users/demoura/papers/CAV2003/index.html
##### Bounded Model Checking and Induction: From Refutation to Verification
In: Proceedings of Computer-Aided Verification, CAV '2003.
Authors
Abstract
We explore the combination of bounded model checking and induction for proving safety properties of infinite-state systems. In particular, we define a general k-induction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are generated from failed k-induction proofs. This strengthening step requires quantifier-elimination, and we propose a lazy quantifier-elimination procedure, which delays expensive computations of disjunctive normal forms when possible. The effectiveness of induction based on bounded model checking and invariant strengthening is demonstrated using infinite-state systems ranging from communication protocols to timed automata and (linear) hybrid automata.
BibTeX Entry
Leonardo de Moura: demoura@csl.sri.com

42. Logic II
Theories, Models, Compactness, completeness examples are added natural numbers with zero and the successor function allow the Quantifier elimination.
http://www1.cuni.cz/~svejdar/courses/logic_ii.html
##### Logic II
Syllabus of the course
(Faculty of Arts and Philosophy, Charles University)
##### Goal of the course
This course is intended for students who already had an introductory courses of logic and of recursion theory. The following knowledge is assumed: syntax and semantics of classical propositional and predicate logic (with equality), Hilbert-style logical calculus, the deduction theorem. Completeness and compactness theorems. Recursive and recursively enumerable sets. Post's theorem, m-reducibility, m-completeness.
PoÂadavky ke zkouÂce jsou dÃ¡ny nÃ¡sledujÃ­cÃ­m sylabem, navÃ­c je tÃ¸eba pÃ¸edloÂit seznam nejmÃ©nÃ¬ dvaceti sedmi vyÃ¸eÂenÃ½ch cviÃ¨enÃ­ z celkem tÃ¸Ã­ dÃ­lÃ¹, viz soubory cvlog1, cvlog2 a cvlog3 dole. Soubor cvlog3 obsahuje sylabus stejnÃ½ jako ten, kterÃ½ nÃ¡sleduje, avÂak v Ã¨eÂtinÃ¬.
##### Gentzen Sequent Calculi
Gentzen sequent calculi can be used to obtain deeper results about provability in Peano arithmetic (e.g. that Peano arithmetic is not finitely axiomatizable) but they are interesting irrespective of other fields. Brief introduction to intuitionistic logic is included because the intuitionistic calculus can be obtained from the classical one by only a small modification and in relevant books (Kleene, Takeuti) both calculi are discussed simultaneously. This part of the course hopefully also throws some more light on the concept of soundness and completeness of calculi in general. The philosophical and historical importance of intuitionistic logic is not discussed. Related notions: sequent, antecedent, succedent, Kripke model.

43. CS 441/541: AI Problem Representation
model assignment of truth or falsity to every possible atom (universe of discourse). Quantifier flipping; finitization for Quantifier elimination
http://web.cecs.pdx.edu/~bart/cs541-fall2000/lectures/2-kr.html
##### AI Problem Representation
PSU CS441/541 Lecture 2
October 2, 2000
• Logical Problem Representation
• Solving a problem with a computer (c.f. Ginsberg 6.1)
• accurately describe problem
• choose instance representation in computer
• select algorithm to manipulate representation
• execute
• What properties of representations are important?
• compactness: must be able to represent big instances efficiently
• utility: must be compatible with good solution algorithms
• soundness: should not report untruths
• completeness: should not lose information
• generality: should be able to represent all or most instances of interesting problems
• transparency: reasoning about/with representation is efficient, easy
• What instance representations do people choose?
• database: collection of facts
• neural net: collection of "neuron weights"
• functional: collection of functions
• logical: collection of sentences
• In achieving properties, support is critical: representations extensively studied, tools available, etc.
• Logic
• Three levels today (see tradeoffs above)
• Propositional Logic: relationship of atomic facts
• Predicate Calculus: relationship of compound facts
• First-Order: relationship of infinite sets of predicates
• The building blocks
• atoms
• propositional atom: identifier (capitalized)
• predicate atom: application of relation to functional argument
• atomic formulae: potentially negated atoms
• sentences: atomic formulae joined by connectives
• negation: not
• conjunction: and
• disjunction: or
• implication: implies
• quantified sentences: introduction of variables

44. Atlas: A Model Based Cut Elimination Proof By Olivier Hermant
If T is a consistent theory, it has a model. THEOREM 2(Cut elimination Theses rewrite systems are known as Quantifier free rewrite systems 3.
http://atlas-conferences.com/c/a/j/y/09.htm
 Atlas home Conferences Abstracts about Atlas Second St.Petersburg Days of Logic and Computability August 24-26, 2003 Petersburg Department of Steklov Institute of Mathematics St. Petersburg, Russia Organizers Sergei ADIAN (Russia), Sergei ARTEMOV (Russia/USA), Nikolai KOSSOVSKI (Russia), Maurice MARGENSTERN (France), Grigori MINTS (USA), Yuri MATIYASEVICH (Russia), the chairman, Nikolai NAGORNY (Russia), Vladimir OREVKOV (Russia), Anatol SLISSENKO (France) View Abstracts Conference Homepage A Model Based Cut Elimination Proof by Olivier Hermant INRIA (Paris, France) INTRODUCTION The sequent calculus modulo, introduced in [1] is a deduction system based on the fact that some axioms can be successfully replaced by rewrite rules on terms an on propositions. This permits to have a faster proof-search and more readable proofs. But in general case, we loose the cut-elimination property that we had for the sequent calculus, the fact that the cut elimination property holds or not depends on the considered rewrite system. On the other hand, we can express with the help of rewrite rules some powerful theories, such as Higher Order Logic [1] or Peano's arithmetic [2]. The paper [1] introduces a proof search system extending resolution for deduction modulo called Extended Narrowing And Resolution (ENAR). This method is proved complete for rewrite systems for which the cut elimination holds. Conversely, in [4] we have proved that the completness of ENAR implies the cut elimination property for sequent calculus modulo the same rewrite system.

45. Efficient Sat-based Unbounded Symbolic Model Checking Invention
0006 The use of SATbased Quantifier elimination through a series of SAT calls has been the focus of Symbolic model Checking algorithm(s) (aka Unbounded
http://www.freshpatents.com/Efficient-sat-based-unbounded-symbolic-model-checkin
Efficient sat-based unbounded symbolic model checking -> Monitor Keywords Title/Abstract/Num. Site Search Search FreshPatents ** File a Provisional Patent ** Site News Monitor Keywords Monitor Archive ... USPTO Class 716
##### Efficient sat-based unbounded symbolic model checking
An efficient approach for SAT-based quantifier elimination and pre-image computation using unrolled designs that significantly improves the performance of pre-image and fix-point computation in SAT-based unbounded symbolic model checking.
Patent Agent: Jeffery J. Brosemer Ph.d., Esq. Holmdel, NJ, US
Patent Inventors: Malay K. Ganai Aarti Gupta Pranav Ashar
Applicaton #: Class: (USPTO)
Related Patents: Data Processing: Design And Analysis Of Circuit Or Semiconductor Mask Circuit Design Translation (e.g., Conversion, Equivalence)
Brief Patent Description Full Patent Description Patent Application Claims
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Provisional Application No. 60/564,174 filed on Apr. 21, 2004, the contents of which are incorporated herein by reference. In addition, this application is related to U.S. patent application Ser. No. 10/157,486, entitled "EFFICIENT APPROACHES FOR BOUNDED MODEL CHECKING," filed on May 30, 2002, the contents of which are incorporated by reference.
FIELD OF THE INVENTION
[0002] The present invention relates generally to techniques for the formal analysis, verification and modeling of digital circuits.

46. FTP 2003 - Abstracts Of Accepted Papers
We exploit Quantifier elimination in the global design of combined . The first version generates about 30000 problems from complete proofs of Mizar
http://www.dsic.upv.es/~rdp03/ftp/abstracts.html
 RDP Home page Organization Sponsors MEETINGS RTA TLCA FTP RULE ... WST VENUE Valencia Registration Accomodation Travelling ... Internet FTP'03 4th International Workshop on First order Theorem Proving Valencia, Spain, June 12-14, 2003 ABSTRACTS OF REGULAR PAPERS ACCEPTED FOR PRESENTATION Quantifier Elimination and Provers Integration S. Ghilardi We exploit quantifier elimination in the global design of combined decision and semi-decision procedures for theories over non-disjoint signatures, thus providing in particular extensions of Nelson-Oppen combination schema. A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions D. Cantone (University of Catania, Italy) J.T. Schwartz (New York University, USA) C.G. Zarba (Stanford University, USA) MLSS is a decidable sublanguage of set theory involving the constructs membership, set equality, set inclusion, union, intersection, set difference, and singleton. In this paper we extend MLSS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We prove that the resulting language is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of MLSS. Canonicity N. Dershowitz

47. On The Complexity Of Quantifier Elimination: The Structural Approach -- Cucker 3
On the Complexity of Quantifier Elimination the Structural Approach More concretely, we give a proof of the existence of NPRcomplete problems.
http://comjnl.oxfordjournals.org/cgi/content/abstract/36/5/400
@import "/resource/css/hw.css"; @import "/resource/css/computer_journal.css"; Skip Navigation Oxford Journals The Computer Journal 1993 36(5):400-408; doi:10.1093/comjnl/36.5.400
British Computer Society

ISI Web of Science (12)
Request Permissions Google Scholar Articles by Cucker, F. Search for Related Content
##### On the Complexity of Quantifier Elimination: the Structural Approach
F. Cucker Universitat Pompeu Fabra, c/ Balmes 132, Barcelona 08008, Spain The aim of this paper is to survey certain theoretical aspects of the complexity of quantifier elimination in the elementary theory of the real numbers with real constants, and to present some new results on the subject. We use the new model of computation

48. Foundations Of Mathematics
Complete theories, compactness theorem, decidability, closed fields, saturated models, Quantifier elimination, prime models
http://sakharov.net/foundation_rt.html
Home Alexander Sakharov Irina Tim Projects Resources Sport Photos Median Logic Math Foundations Badminton Clubs Trip Photos ... Downloads
##### - Textbook / Reference -
with contributions by Bhupinder Anand Harvey Friedman Haim Gaifman Vladik Kreinovich ... Stephen Simpson
featured in the Computers/Mathematics section of Science Magazine NetWatch

 49. Intute: Science, Engineering And Technology - Search Results Topics in this course include sentences and models, complete theories, . the elimination of quantifiers, Galois theory and saturated models,http://www.intute.ac.uk/sciences/cgi-bin/search.pl?term1=model theory&limit=0

 50. On The Complexity Of Quantifier Elimination The Structural Approach On the Complexity of Quantifier Elimination the Structural Approach More concretely, we give a proof of the existence of NPR complete problems.http://csep.hpcc.nectec.or.th/Journals/oup/smj/journals/ed/titles/computer_journ

51. Abstracts Of Malika More
The problem SAT of CNFSatisfiability is the prototype of NP-complete problems. . Malika More, Nicole Schweikardt, On Quantifier elimination in weak
http://laic.u-clermont1.fr/~more/recherche/abstract2.html
##### Abstracts of some papers
Malika More, Investigation of binary spectra by explicit transformations of graphs Theoretical Computer Science , 124, pp. 221-272, 1994 (Fundamental Study) Abstract :
Let L be the first-order language with identity whose set of specific symbols consists of the binary predicate symbols R_1, ..., R_q. Let A be an L-sentence and let us denote by Gen(A) (generalized spectrum of A) the set of all finite models of A. We say that A represents gen(A). The spectrum S(A) of sentence A is the set of cardinalities of domains of elements of Gen(A) and A is also called a representation of S(A). Let A be some L-sentence and P be a polynomial of degree k of Z[X] asymtotically greater than or equal to identity function on N. We produce a sentence P(A) representing P(S(A)), i.e. S(P(A))=P(S(A)). The algorithm producing P(A) depends only on P and L and effectively one-to-one maps elements of Gen(A) onto elements of Gen(P(A)). This sentence P(A) is formalized in a binary language L* of cardinality 2q+k if k

52. Applications Of Quantified Constraint Solving Over The Reals
The list is certainly not complete, but grows as the author encounters new items. On solving semidefinite programming by Quantifier elimination.
http://www.cs.cas.cz/~ratschan/appqcs.html
##### January 2, 2007
Quantified constraints over the reals appear in numerous contexts. Usually existential quantification occurs when some parameter can be chosen by the user of a system, and univeral quantification when the exact value of a parameter is either unknown, or when it occurs in infinitely many, similar versions. The following is a list of application areas and publications that contain applications for solving quantified constraints over the reals. The list is certainly not complete, but grows as the author encounters new items. Contributions are very welcome!
Electrical Engineering/Electronics:
Stability:
Control:
, survey , reachability , embedded control systems , hybrid systems , projection of system output function , computation of control invariant sets
Computational Geometry/Motion Planning/Collision Detection:
Constraint Databases:
Theorem Proving in Real Geometry:
Several Different:
Use of Predicate Language for Modeling Engineering Problems:
Other:
camera motion: , constraint logic programming: , mechanical engineering: , mathematics: (from , biology: , interpolation: , scheduling , automated theorem proving , optimization: , termination of rewrite systems , flight control , program analysis , hybrid systems , injectivity test (see Lagrange/Delanoue/Jaulin papers), computer assisted proofs

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