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An introduction to Gödel's Theorems

作者: Peter Smith
出版商: Cambridge : Cambridge University Press, 2007.
叢書: Cambridge introductions to philosophy.
版本/格式:   圖書 : 英語所有版本和格式的總覽
資料庫:WorldCat
提要:
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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類型/形式: Einführung
提及的人: Kurt Gödel; Kurt Gödel
資料類型: 網際網路資源
文件類型: 圖書, 網路資源
所有的作者/貢獻者: Peter Smith
ISBN: 9780521857840 0521857848 9780521674539 0521674530
OCLC系統控制編碼: 124025603
描述: xiv, 361 p. ; 26 cm.
内容: 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.
叢書名: Cambridge introductions to philosophy.
責任: Peter Smith.
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摘要:

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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