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An introduction to Gödel's Theorems

Author: Peter Smith
Publisher: Cambridge : Cambridge University Press, 2007.
Series: Cambridge introductions to philosophy.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Peter Smith examines Gödel's Theorems, how they were established and why they matter. This is an ideal textbook for philosophy and mathematics students taking a first course in mathematical logic. A companion website is included with exercises.
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Details

Genre/Form: Einführung
Named Person: Kurt Gödel; Kurt Gödel
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter Smith
ISBN: 9780521857840 0521857848 9780521674539 0521674530
OCLC Number: 124025603
Description: xiv, 361 p. ; 26 cm.
Contents: What Godel's theorems say --
Decidability and enumerability --
Axiomatized formal theories --
Capturing numerical properties --
The truths of arithmetic --
Sufficiently strong arithmetics --
Interlude: taking stock --
Two formalized arithmetics --
What q can prove --
First-order peano arithmetic --
Primitive recursive functions --
Capturing p r functions --
Q is p.r. adequate --
Interlude: a very little about Principia --
The arithmetization of syntax --
PA is incomplete --
Godel's first theorem --
Interlude: about the first theorem --
Strengthening the first theorem --
The diagonalization lemma --
Using the diagonalization lemma --
Second-order arithmetics --
Interlude: incompleteness and Isaacson's conjecture --
Godel's second theorem for PA --
The derivability conditions --
Deriving the derivability conditions --
Reflections --
Interlude: about the second theorem --
Recursive functions --
Undecidability and incompleteness --
Turing machines --
Turing machines and recursiveness --
Halting problems --
The church-turing thesis --
Proving the thesis.
Series Title: Cambridge introductions to philosophy.
Responsibility: Peter Smith.
More information:

Abstract:

Peter Smith examines Gödel's Theorems, how they were established and why they matter. This is an ideal textbook for philosophy and mathematics students taking a first course in mathematical logic. A companion website is included with exercises.

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