Elements of Mathematical Logic
(Model Theory)
Published on 14. May 2014
235 pages
978-0-08-095767-8 (ISBN)
Description
Elements of Mathematical Logic
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Lev D. Beklemishev
Provability, Computability and Reflection: Volume 48
Book
04/2000
Elsevier
€210.46
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Content
- 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 types
- Predicate 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 order
- Infinite 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 terms
- 2. 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
