Preface to the Second Edition
Preface to the First Edition
Ⅰ PROVABILITY
Ⅰ Introduction to Formal Languages
1 General Information
2 First-Order Languages
Digression: Names
3 Beginners' Course in Translation
Digression: Syntax
Ⅱ Truth and Deducibility
1 Unique Reading Lemma
2 Interpretation: Truth, Definability
3 Syntactic Properties of Truth
Digression: Natural Logic
4 Deducibility
Digression: Proof
5 Tautologies and Boolean Algebras
Digression: Kennings
6 Godel's Completeness Theorem
7 Countable Models and Skolem's Paradox
8 Language Extensions
9 Undefinability of Truth: The Language SELF
10 Smullyan's Language of Arithmetic
11 Undefinability of Truth: Tarski's Theorem
Digression: Self-Reference
12 Quantum Logic
Appendix: The Von Neumann Universe
The Last Digression. Truth as Value and Duty: Lessons of Mathematics
Ⅲ The Continuum Problem and Forcing
1 The Problem: Results, Ideas
2 A Language of Real Analysis
3 The Continuum Hypothesis Is Not Deducible in L2 Real
4 Boolean-Valued Universes
5 The Axiom of Extensionality Is "True"
6 The Axioms of Pairing, Union, Power Set, and Regularity Are "True"
7 The Axioms of Infinity, Replacement, and Choice Are "True".
8 The Continuum Hypothesis Is "False" for Suitable B
9 Forcing
Ⅳ The Continuum Problem and Constructible Sets
1 Godel's Constructible Universe
2 Definability and Absoluteness
3 The Constructible Universe as a Model for Set Theory
4 The Generalized Continuum Hypothesis Is L-True
5 Constructibility Formula
6 Remarks on Formalization
7 What Is the Cardinality of the Continuum?
Ⅱ COMPUTABILITY
Ⅴ Recursive Functions and Church's Thesis
1 Introduction. Intuitive Computability
2 Partial Recursive Functions
