skip to content
An introduction to Gödel's Theorems Preview this item
ClosePreview this item
Checking...

An introduction to Gödel's Theorems

Author: Peter Smith
Publisher: Cambridge : Cambridge University Press, 2007.
Series: Cambridge introductions to philosophy.
Edition/Format:   Print 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.
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

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 pages ; 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.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/124025603> # An introduction to Gödel's Theorems
    a schema:CreativeWork, schema:Book ;
    library:oclcnum "124025603" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/enk> ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/119737250#Place/cambridge> ; # Cambridge
    schema:about <http://dewey.info/class/511.3/e22/> ;
    schema:about <http://viaf.org/viaf/97851774> ; # Kurt Gödel
    schema:about <http://experiment.worldcat.org/entity/work/data/119737250#Topic/godelscher_unvollstandigkeitssatz> ; # Gödelscher Unvollständigkeitssatz
    schema:about <http://experiment.worldcat.org/entity/work/data/119737250#Topic/logic_symbolic_and_mathematical> ; # Logic, Symbolic and mathematical
    schema:bookFormat bgn:PrintBook ;
    schema:creator <http://viaf.org/viaf/163091330> ; # Peter Smith
    schema:datePublished "2007" ;
    schema:description "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."@en ;
    schema:description "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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/119737250> ;
    schema:genre "Einführung"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/119737250#Series/cambridge_introductions_to_philosophy> ; # Cambridge introductions to philosophy.
    schema:name "An introduction to Gödel's Theorems"@en ;
    schema:productID "124025603" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/124025603#PublicationEvent/cambridge_cambridge_university_press_2007> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/119737250#Agent/cambridge_university_press> ; # Cambridge University Press
    schema:url <http://catdir.loc.gov/catdir/enhancements/fy0803/2007299862-t.html> ;
    schema:workExample <http://worldcat.org/isbn/9780521857840> ;
    schema:workExample <http://worldcat.org/isbn/9780521674539> ;
    umbel:isLike <http://bnb.data.bl.uk/id/resource/GBA733037> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/124025603> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/119737250#Agent/cambridge_university_press> # Cambridge University Press
    a bgn:Agent ;
    schema:name "Cambridge University Press" ;
    .

<http://experiment.worldcat.org/entity/work/data/119737250#Series/cambridge_introductions_to_philosophy> # Cambridge introductions to philosophy.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/124025603> ; # An introduction to Gödel's Theorems
    schema:name "Cambridge introductions to philosophy." ;
    schema:name "Cambridge introductions to philosophy" ;
    .

<http://experiment.worldcat.org/entity/work/data/119737250#Topic/godelscher_unvollstandigkeitssatz> # Gödelscher Unvollständigkeitssatz
    a schema:Intangible ;
    schema:name "Gödelscher Unvollständigkeitssatz"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/119737250#Topic/logic_symbolic_and_mathematical> # Logic, Symbolic and mathematical
    a schema:Intangible ;
    schema:name "Logic, Symbolic and mathematical"@en ;
    .

<http://viaf.org/viaf/163091330> # Peter Smith
    a schema:Person ;
    schema:birthDate "1944" ;
    schema:familyName "Smith" ;
    schema:givenName "Peter" ;
    schema:name "Peter Smith" ;
    .

<http://viaf.org/viaf/97851774> # Kurt Gödel
    a schema:Person ;
    schema:familyName "Gödel" ;
    schema:givenName "Kurt" ;
    schema:name "Kurt Gödel" ;
    .

<http://worldcat.org/isbn/9780521674539>
    a schema:ProductModel ;
    schema:isbn "0521674530" ;
    schema:isbn "9780521674539" ;
    .

<http://worldcat.org/isbn/9780521857840>
    a schema:ProductModel ;
    schema:isbn "0521857848" ;
    schema:isbn "9780521857840" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.