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全新正版数理逻辑(第2版)(英文版)9787519255725世界图书出版公司
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Preface
PART A
I Introduction
1.An Example from Group Theory
2.An Example from the Theory of Equivalence Relations
3.A Preliminary Analysis
4.Preview
II Syntax of First-Order Languages
1. Alphabets
2.The Alphabet of a First-Order Language
3.Terms and Formulas in First-Order Languages
4.Induction in the Calculus of Terms and in the Calculus of Formulas
5.Free Variables and Sentences
III Semantics of First-Order Languages
1.Structures and Interpretations
2.Standardization of Connectives
3.The Satisfaction Relation
4.The Consequence Relation
5.Two Lemmas on the Satisfaction Relation
6.Some Simple Formalizations
7.Some Remarks on Formalizability
8.Substitution
IV A Sequent Calculus
1.Sequent Rules
2.Structural Rules and Connective Rules
3.Derivable Connective Rules
4.ntifier and Equality Rules
5.Further Derivable Rules and Sequents
6.Summary and Example
7.Consistency
V The Comleess Theorem
1.Henkin's Theorem
2.Satisfiability of Consistent Sets of Formulas (the Countable Case)
3.Satisfiability of Consistent Sets of Formulas (the General Case)
4.The Comleess Theorem
VI The Lowenheim-Skolem and the Compactness Theorem
1.The Lowenheim-Skolem Theorem
2.The Compactness Theorem
3.Elementary Classes
4.Elementarily Equivalent Structures
VII The Scope of First-Order Logic
1.The Notion of Formal Proof
2.Mathematics Within the Framework of First-Order Logic
3.The Zermelo-Fraenkel Axioms for Set Theory
4.Set Theory as a Basis for Mathematics
VIII Syntactic Interpretations and Normal Forms
1.Term-Reduced Formulas and Relational Symbol Sets
2.Syntactic Interpretations
3.Extensions by Definitions
4.Normal Forms
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