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Mathematical Logic

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ISBN-10: 1568811357

ISBN-13: 9781568811352

Edition: 2nd 2001

Authors: Joseph R. Shoenfield

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Book details

Edition: 2nd
Copyright year: 2001
Publisher: A K Peters, Limited
Publication date: 2/9/2001
Binding: Paperback
Pages: 356
Size: 6.75" wide x 9.50" long x 0.75" tall
Weight: 1.144
Language: English

The Nature of Mathematical Logic
Axiom systems
Formal systems
Syntactical variables
First-Order Theories
Functions and predicates
Truth functions
Variables and quantifiers
First-order languages
Structures
Logical axioms and rules
Problems
Theorems in First-Order Theories
The tautology theorem
Results on quantifiers
The deduction theorem
The equivalence and equality theorems
Prenex form
Problems
The Characterization Problem
The reduction theorem
The completeness theorem
The consistency theorem
Herbrand's theorem
Addition of function symbols
Extensions by definitions
Interpretations
Problems
The Theory of Models
The compactness theorem
Isomorphisms and substructures
Cardinality of models
Joint consistency
Complete theories
Categoricity
Problems
Incompleteness and Undecidability
Calculability
Recursive functions
Explicit definitions
Sequence numbers
Church's thesis
Expression numbers
Representability
Church's theorem and the incompleteness theorem
Undecidability
Problems
Recursion Theory
Partial functions
Functionals and relations
Properties of recursive functionals
Indices
The arithmetical hierarchy
Relative recursiveness
Degrees
The analytical hierarchy
Hyperarithmetical relations
The characterization theorem
Basis theorems
Problems
The Natural Numbers
Peano arithmetic
The theorem on consistency proofs
The consistency proof
Applications of the consistency proof
Second-order arithmetic
Problems
Set Theory
Axioms for sets
Development of set theory
Ordinals
Cardinals
Interpretations of set theory
Constructible sets
The axiom of constructibility
Forcing
The independence proofs
Large cardinals
Problems
The Word Problem
Index
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