Introduction to the Theory of Logic

ISBN-10: 081336602X

ISBN-13: 9780813366029

Edition: 2000

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Book details

List price: $48.00
Copyright year: 2000
Publisher: Westview Press
Publication date: 1/12/2000
Binding: Paperback
Pages: 344
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 0.990
Language: English

Preface
The Elements
Introduction
Extensionality
Sets
Mathematical Proof
Relations
Some Binary Relations
Equivalence Relations
Orderings
Functions
Numbers
Propositional Logic
Introduction
Induction and Formal Languages
Syntax
Semantics
Unique Readability
Recursive Definitions
Expressive Completeness
Expressively Complete Languages
First-Order Logic: Syntax and Semantics
Introduction
Properties, Relations and Individuals
Truth-Functional Composition
Functions
Identity
Quantification
Syntax
Semantics
Truth
Logical Consequence and Other Logical Notions
Models
Equivalence Relations
Orderings
Structures for the First-Order Language with No Extralogical Symbols
Groups
Arithmetic
Deduction
Introduction
The Basic Rule and the Connective Rules
Propositional Deduction
Substitution
Quantifier and Identity Rules
Establishing (First-Order) Deducibility Claims
The Definition of Deducibility
Deducibility in Different Languages
Soundness and Completeness
Soundness
Completeness, Consistency and Model Existence
Canonical Structures and Well-Rounded Sets, I: First-Order Languages without Identity
Canonical Structures and Well-Rounded Sets, II: First-Order Languages with Identity
A Well-Rounded Set of Sentences Is the Theory of its Canonical Structure
Negation Completeness
Henkin Constants and Henkin Axioms
Consistent, Negation-Complete Henkin Sets Are Well Rounded
Compactness
Cardinality
The Size of Infinity
Criteria for Size Claims
Counting
Functional Criteria
Same Size
Big and Small
Addition
Multiplication
Exponentiation
Cardinality
Contextual Definition
Continuities
Denumerable Sets
Diagonals
ZF
Choice
Zorn's Lemma
Completeness for Uncountable Languages
Expressive Limitations
Representation and Indiscernibility
Isomorphic Structures
Isomorphic Structures and Contextual Definitions
Representing Finite Structures
The Downward Lowenheim-Skolem Theorem
Skolem's Paradox
The Upward Lowenheim-Skolem Theorem
Finite Structures Again
Nonstandard Models of Arithmetic
Strict Dense Linear Orderings with no Minimal or Maximal Elements
Categoricity in Power
Decidability
Decidable Sets of Sentences and Indiscernible Structures
Vaught's Test
Strict Dense Linear Orderings with No Minimal or Maximal Elements
Successor Arithmetic
Quantifier Elimination
Strict Dense Linear Orderings with No Minimal or Maximal Elements
Successor Arithmetic
Ordered Successor Arithmetic
The Decision Problem
Decidable Structures
Godel's First Incompleteness Theorem
Set Theory Revisited
Symbols and Notation
Greek Letters
Index
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