دانلود کتاب A Friendly Introduction to Mathematical Logic

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Contents
Preface
1. Structures and Languages
1.1 Naïvely
1.2 Languages
1.3 Terms and Formulas
1.4 Induction
1.5 Sentences
1.6 Structures
1.7 Truth in a Structure
1.8 Substitutions and Substitutability
1.9 Logical Implication
1.10 Summing Up, Looking Ahead
2. Deductions
2.1 Naïvely
2.2 Deductions
2.3 The Logical Axioms
2.4 Rules of Inference
2.5 Soundness
2.6 Two Technical Lemmas
2.7 Properties of Our Deductive System
2.8 Nonlogical Axioms
2.8 Summing Up, Looking Ahead
3. Completeness and Compactness
3.1 Naïvely
3.2 Completeness
3.3 Compactness
3.4 Substructures and the Löwenheim–Skolem Theorems
3.5 Summing Up, Looking Ahead
4. Incompleteness from Two Points of View
4.1 Introduction
4.2 Complexity of Formulas
4.3 The Roadmap to Incompleteness
4.4 An Alternate Route
4.5 How to Code a Sequence of Numbers
4.6 An Old Friend
4.7 Summing Up, Looking Ahead
5. Syntactic Incompleteness—Groundwork
5.1 Introduction
5.2 The Language, the Structure, and the Axioms of N
5.3 Representable Sets and Functions
5.4 Representable Functions and Computer Programs
5.5 Coding—Naïvely
5.6 Coding Is Representable
5.7 Gödel Numbering
5.8 Gödel Numbers and N
5.9 Num and Sub Are Representable
5.10 Definitions by Recursion Are Representable
5.11 The Collection of Axioms Is Representable
5.12 Coding Deductions
5.13 Summing Up, Looking Ahead
6. The Incompleteness Theorems
6.1 Introduction
6.2 The Self-Reference Lemma
6.3 The First Incompleteness Theorem
6.4 Extensions and Refinements of Incompleteness
6.5 Another Proof of Incompleteness
6.6 Peano Arithmetic and the Second Incompleteness Theorem
6.7 Summing Up, Looking Ahead
7. Computability Theory
7.1 The Origin of Computability Theory
7.2 The Basics
7.3 Primitive Recursion
7.4 Computable Functions and Computable Indices
7.5 The Proof of Kleene\'s Normal Form Theorem.
7.6 Semi-Computable and Computably Enumerable Sets
7.7 Applications to First-Order Logic
7.8 More on Undecidability
8. Summing Up, Looking Ahead
8.1 Once More, With Feeling
8.2 The Language ℒ_{BT} and the Structure