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Elements of mathematical logic : (model theory).

Author: G Kreisel; J L Krivine
Publisher: Burlington : Elsevier, 2000.
Series: Studies in logic and the foundations of mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Provability, Computability and Reflection.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kreisel, G.
Elements of mathematical logic : (model theory).
Burlington : Elsevier, ©2000
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: G Kreisel; J L Krivine
ISBN: 9780080957678 0080957676
OCLC Number: 813230007
Description: 1 online resource (235 pages).
Contents: Front Cover; Elements of Mathematical Logic; Copyright Page; CONTENTS; Chapter 0. Preliminaries: Definition schemas; Chapter 1. Propositional calculus; Exercises; Chapter 2. Predicate calculus; Exercises; Chapter 3. Predicate calculus with equality; Exercises; Chapter 4. Elimination of quantifiers; Dense orders with first and last element; Discrete orders without first or last element; Some commutative groups with discrete total orderings; Algebraically closed fields; Real closed fields; Seperable Boolean rings; Exercises. Chapter 5. Predicate calculus with several types of objects: the hierarchy of finite typesPredicate calculus with equality, with k types of objects, without function symbols; Predicate calculus with equality. with k types of objects. including function symbols; Finite type structure; Hierarchy of finite types; Principal models; Exercises; Chapter 6. Definability; Invariance and stability; Invariance and stability: hierarchy of finite types; Rigidity; Definability in C-realizations; Exercises; Chapter 7. Principal models: models of infinite formulas; Principal models: formulas of finite order. Principal models: some formulas of second orderInfinite formulas which define finitary relations; CountabIe languages: countable sets of infinite formulas; Exercises; Appendix I. The axiomatic method; Appendix II. Foundations of mathematics; Part A: Set-theoretic semantic foundations; 1. Analysis of intuitive mathematics in set-theoretic terms; 2. Formulation of laws for the basic set-theoretic notions; 3. New axioms for the set-theoretic notions: axioms of infinity; 4. Analysis of the intuitive notion of logical validity; Part B: Combinatorial foundations; 0. Combinatorial reasoning. 1. Analysis of intuitive mathematics in combinatorial terms2. Formulation of laws for the basic combinatorial notions; 3. Developments of the theory; 4. Critical discussion; Part C: Semantic versus syntactic (combinatorial) introduction to mathematical logic; mathematical logic.
Series Title: Studies in logic and the foundations of mathematics.

Abstract:

Provability, Computability and Reflection.

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