دانلود کتاب An Introduction to Mathematical Logic

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Preface
Contents
Chapter 1 Mathematics and Reality
1-1 Abstract or applied
1-2 Definitions and undefined expressions
1-3 Unproved statements
1-4 Models and interpretations
1-5 Where do little axioms come from?
1-6 Mathematical systems
1-7 The plan of this book
Chapter 2 Sentential Variables, Operators, and Formulas
2-1 Introduction
2-2 Sentential variables and sentential formulas
2-3 Negation
2-4 Conjunction and disjunction
2-5 The conditional
2-6 The biconditional
2-7 Brackets and scope conventions. Sentential operators
Chapter 3 Truth Tables. The Sentential Calculus
3-1 Basic truth tables
3-2 Truth tables for compound sentences
3-3 Tautologies
3-4 A short test for tautology
3-5 Choice of formulas
3-6 Useful tautological formulas
3-7 Reducing the number of basic operators
Chapter 4 The Deeper Structure of Statements
4-1 Quantifiers
4-2 The significance of quantifiers
4-3 Purifying quantifiers
4-4 Atomic statements
4-5 Terms
4-6 Constants aiu1 variables
4-7 Bound variables and free variables
4-8 Predicate notation
4-9 Special pairs of statement forms
Chapter 5 The Demonstration
5-1 Introduction
5-2 The turnstile
5-3 Rules of assumption and tautology
5-4 Rules of instance and example
5-5 Rules of choice and generalization. Specified variables
5-6 Rules of reflexivity of equality, equality substitution, and biconditional substitution
5-7 Rule of detachment
5-8 Presenting a demonstration
5-9 Three sample demonstrations
5-10 Equivalence relations
Chapter 6 Two Major Theorems
6-1 Introduction
6-2 The lemma theorem
6-3 The general deduction theorem
6-4 Three corollaries
Chapter 7 Supplementary Inference Rules
7-1 The inference rule symbol
7-2 The pattern of proof for new inference rules
7-3 Inference rule forms of the rules of instance, example, choice, generalization, equality substitution, and biconditional substitution
7-4 Iterated use of the rules of instance and example
7-5 The tautological inference family
7-6 Generalized versions of certain rules
Chapter 8 Universal Theorems
8-1 Introduction
8-2 Some particularly useful universal theorems
8-3 Equality as an equivalence relation
8-4 Formal proof
8-5 Applications in group theory
Chapter 9 Techniques of Negation
9-1 Motivation
9-2 The basic relations and their applications
Chapter 10 Terms and Definitions
10-1 Variables as terms
10-2 Other terms
10-3 Terms by postulate
10-4 Terms by substitution
10-5 Terms by definition
10-6 Constants
10-7 Defining new statement forms
10-8 Definitions and the demonstration
10-9 More formal versions of four basic rules
10-10 A theorem on equality
Chapter 11 The System {/|, ∈}
11-1 Introduction
11-2 Undefined expressions
11-3 Criteria for statements
11-4 Axioms and definitions
11-5 Some simple basic theorems
11-6 Membership and equality
11-7 Subset theorems and tautologies
11-8 Illustrative proofs
Chapter 12 The Boolean Approach: the System {/|, ∩, ∪}
12-1 Introduction
12-2 Axioms and definitions
12-3 A list of theorems
12-4 Moves toward informality
12-5 The duality principle for {/|, ∩, ∪}
Answers to Odd-Numbered Exercises
Index