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Mathematical Logic

ISBN-10: 0486425339

ISBN-13: 9780486425337

Edition: 2002 (Unabridged)

Authors: Stephen Cole Kleene

List price: $24.95
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Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the 20th century's greatest authorities on the subject.
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Book details

List price: $24.95
Copyright year: 2002
Publisher: Dover Publications, Incorporated
Publication date: 12/18/2002
Binding: Hardcover
Pages: 416
Size: 5.50" wide x 8.25" long x 1.00" tall
Weight: 0.990
Language: English

Elementary Mathematical Logic
The propositional calculus
Linguistic considerations: formulas
Model theory: truth tables, validity
Model theory: the substitution rule, a collection of valid formulas
Model theory: implication and equivalence
Model theory: chains of equivalences
Model theory: duality
Model theory: valid consequence
Model theory: condensed truth tables
Proof theory: provability and deducibility
Proof theory: the deduction theorem
Proof theory: consistency, introduction and elimination rules
Proof theory: completeness
Proof theory: use of derived rules
Applications to ordinary language: analysis of arguments
Applications to ordinary language: incompletely stated arguments
The predicate calculus
Linguistic considerations: formulas, free and bound occurrences of variables
Model theory: domains, validity
Model theory: basic results on validity
Model theory: further results on validity
Model theory: valid consequence
Proof theory: provability and deducibility
Proof theory: the deduction theorem
Proof theory: consistency, introduction and elimination rules
Proof theory: replacement, chains of equivalences
Proof theory: alterations of quantifiers, prenex form
Applications to ordinary language: sets, Aristotelian categorical forms
Applications to ordinary language: more on translating words into symbols
The predicate calculus with equality
Functions, terms
Equality vs. equivalence, extensionality
Mathematical Logic and the Foundations of Mathematics
The foundations of mathematics
Countable sets
Cantor's diagonal method
Abstract sets
The paradoxes
Axiomatic thinking vs. intuitive thinking in mathematics
Formal systems, metamathematics
Formal number theory
Some other formal systems
Computability and decidability
Decision and computation procedures
Turing machines, Church's thesis
Church's theorem (via Turing machines)
Applications to formal number theory: undecidability (Church) and incompleteness (Godel's theorem)
Applications to formal number theory: consistency proofs (Godel's second theorem)
Application to the predicate calculus (Church, Turing)
Degrees of unsolvability (Post), hierarchies (Kleene, Mostowski)
Undecidability and incompleteness using only simple consistency (Rosser)
The predicate calculus (additional topics)
Godel's completeness theorem: introduction
Godel's completeness theorem: the basic discovery
Godel's completeness theorem with a Gentzen-type formal system, the Lowenheim-Skolem theorem
Godel's completeness theorem (with a Hilbert-type formal system)
Godel's completeness theorem, and the Lowenheim-Skolem theorem, in the predicate calculus with equality
Skolem's paradox and nonstandard models of arithmetic
Gentzen's theorem
Permutability, Herbrand's theorem
Craig's interpolation theorem
Beth's theorem on definability, Robinson's consistency theorem
Theorem and lemma numbers: pages
List of postulates
Symbols and notations