Introduction to Model Theory and to the Metamathematics of Algebra
Published on 14. May 2014
295 pages
978-0-08-095752-4 (ISBN)
Description
Provability, Computability and Reflection
More details
Other editions
Additional editions
Lev D. Beklemishev
Provability, Computability and Reflection: Volume 32
Book
04/2000
Elsevier
€210.46
Article exhausted; check different version
Content
- Front Cover
- Introduction to Model Theory and to The Metamathematics of Algebra
- Copyright Page
- List of Contents
- CHAPTER I. THE LOWER PREDICATE CALCULUS
- 1.1. General introduction
- 1.2. Rules of formation
- 1.3. Rules of deduction
- 1.4. Semantic interpretation
- 1.5. The relation between deductive and descriptive concepts
- 1.6. Sets of sentences and their varieties
- 1.7. Problems
- CHAPTER II. ALGEBRAIC THEORIES
- 2.1. Equality
- 2.2. Specification of axiomatic systems
- 2.3. Related sets of sentences
- 2.4. Embedding theorems and transfer principles
- 2.5. Malcev's theory of normal chains
- 2.6. Problems
- CHAPTER III. SOME CONCEPTS AND METHODS OF MODEL THEORY
- 3.1. Skolem functions
- relativization
- 3.2. The extension of models
- 3.3. The prefix problem
- 3.4. Obstructions to arithmetical extension
- 3.5. Convex systems
- 3.6. Model-consistency
- 3.7. Problems
- CHAPTER IV. COMPLETENESS
- 4.1. A test for completeness
- 4.2. Model-completeness
- 4.3. Relative model-completeness
- 4.4. Problems
- CHAPTER V. DEFINABILITY
- 5.1. The consistency lemma
- 5.2. Beth's theorem
- 5.3. Relative definitions
- 5.4. Application to the Nullstellensatz
- 5.5. Model-completion
- 5.6. Problems
- CHAPTER VI. GENERALIZATION OF ALGEBRAIC CONCEPTS
- 6.1. Polynomials in general axiomatic systems
- 6.2. Bounded predicates
- 6.3. Algebraic predicates
- 6.4. Algebraic predicates and convex systems
- 6.5. Separability
- 6.6. Problems
- CHAPTER VII. METAMATHEMATICAL THEORY OF IDEALS
- 7.1. Introduction
- 7.2. Metamathematical ideals
- 7.3. Connection between ideals in different domains
- 7.4. Disjunctive ideals
- 7.5. Ideals and homomorphisms
- 7.6. Problems
- CHAPTER VIII. METAMATHEMATICAL THEORY OF VARIETIES
- 8.1. Varieties of structures
- 8.2. Pre-ideals and their varieties
- 8.3. Metamathematical varieties and algebraic varieties
- 8.4. Differential ideals
- 8.5. Hilbert's seventeenth problem
- 8.6. Problems
- CHAPTER IX. SELECTED TOPICS
- 9.1. Introduction of function symbols
- 9.2. The elimination of quantifiers
- 9.3. Direct products and ultraproducts
- 9.4. Non-standard analysis
- 9.5. Non-standard theory of functions of a real variable
- 9.6. Non-standard analysis of functions of several variables
- 9.7. Problems
- BIBLIOGRAPHY
- INDEX OF AUTHORS
- SUBJECT INDEX
