An introduction to Gödel's Theorems /
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| Author / Creator: | Smith, Peter, 1944- |
|---|---|
| Imprint: | Cambridge : Cambridge University Press, 2007. |
| Description: | xiv, 361 p. ; 26 cm. |
| Language: | English |
| Series: | Cambridge introductions to philosophy Cambridge introductions to philosophy. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6616001 |
MARC
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| 100 | 1 | |a Smith, Peter, |d 1944- |0 http://id.loc.gov/authorities/names/n86102736 |1 http://viaf.org/viaf/46145602393201360589 | |
| 245 | 1 | 3 | |a An introduction to Gödel's Theorems / |c Peter Smith. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2007. | ||
| 300 | |a xiv, 361 p. ; |c 26 cm. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 490 | 1 | |a Cambridge introductions to philosophy | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 600 | 1 | 0 | |a Gödel, Kurt. |0 http://id.loc.gov/authorities/names/n79007770 |1 http://viaf.org/viaf/97851774 |
| 650 | 0 | |a Logic, Symbolic and mathematical. |0 http://id.loc.gov/authorities/subjects/sh85078115 | |
| 650 | 0 | 7 | |a Gödelscher Unvollständigkeitssatz. |2 swd |
| 655 | 7 | |a Einführung. |2 swd | |
| 655 | 4 | |a Einführung. | |
| 600 | 1 | 7 | |a Gödel, Kurt. |2 fast |0 http://id.worldcat.org/fast/fst00030398 |0 http://id.worldcat.org/fast/30398 |1 http://viaf.org/viaf/97851774 |
| 650 | 7 | |a Gödel numbers. |2 fast |0 http://id.worldcat.org/fast/fst00949805 | |
| 650 | 7 | |a Logic, Symbolic and mathematical. |2 fast |0 http://id.worldcat.org/fast/fst01002068 | |
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| 927 | |t Library of Congress classification |a QA9.65 .S65 2007 |l Eck |c Eck-Eck |e VAND |b 77110762 |i 8266206 | ||
