Introduction to Model Theory and to the Metamathematics of Algebra

Name: Introduction to Model Theory and to the Metamathematics of Algebra
Brand: Elsevier
Price: 215.0 EUR
Availability: OnlineOnly

Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

295 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-0-08-095752-4 (ISBN)

215,00 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

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

Systemvoraussetzungen

Als PDF speichern Als Link merken