About: Proof sketch for Gödel's first incompleteness theorem

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This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses, which are discussed as needed during the sketch. We will assume for the remainder of the article that a fixed theory satisfying these hypotheses has been selected. Throughout this article the word "number" refers to a natural number. The key property these numbers possess is that any natural number can be obtained by starting with the number 0 and adding 1 a finite number of times.

Attributes	Values
rdf:type	yago:WikicatMathematicalProofs yago:Abstraction100002137 yago:Argument106648724 yago:Communication100033020 yago:Evidence106643408 yago:Indication106797169 yago:MathematicalProof106647864 yago:Proof106647614
rdfs:label	Beweise der gödelschen Unvollständigkeitssätze (de) Proof sketch for Gödel's first incompleteness theorem (en)
rdfs:comment	Dieser Artikel skizziert Beweise der Gödelschen Unvollständigkeitssätze. Dabei handelt es sich um zwei mathematische Sätze, die zu den wichtigsten Ergebnissen der Logik gezählt werden und die von Kurt Gödel 1930 bewiesen wurden. Der erste Unvollständigkeitssatz besagt, dass kein konsistentes Axiomensystem, dessen Theoreme von einem Algorithmus aufgezählt werden können, alle wahren Aussagen über natürliche Zahlen mit Addition und Multiplikation beweisen kann. Der zweite Unvollständigkeitssatz besagt, dass ein solches System die eigene Widerspruchsfreiheit nicht beweisen kann. (de) This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses, which are discussed as needed during the sketch. We will assume for the remainder of the article that a fixed theory satisfying these hypotheses has been selected. Throughout this article the word "number" refers to a natural number. The key property these numbers possess is that any natural number can be obtained by starting with the number 0 and adding 1 a finite number of times. (en)
dcterms:subject	Mathematical proofs Mathematical logic
Wikipage page ID	9142932 (xsd:integer)
Wikipage revision ID	1106008895 (xsd:integer)
Link from a Wikipage to another Wikipage	Primitive recursive function Model theory Algorithm Peano Arithmetic Peano arithmetic Peano axioms Commutativity Consistency Consistent George Boolos Theorem Successor (graph theory) Completeness (logic) Successor function Gödel, Escher, Bach Robinson arithmetic ASCII First-order logic Number theory Berry's paradox Diagonal lemma Formal system Logical connective Free variable Well-formed formula Quantifier (logic) Recursion Recursively enumerable Gödel's incompleteness theorems Jean van Heijenoort Mathematical proofs Mathematical logic Domain of discourse Douglas Hofstadter Solomon Feferman Iff Natural number Signature (logic) Consistency proof Completeness theorem Gödel number Gödel sentence Existential quantifier Omega-consistent
Link from a Wikipage to an external page	http://hirzels.com/martin/papers/canon00-goedel.pdf http://www.apronus.com/math/goedel.htm
sameAs	Proof sketch for Gödel's first incompleteness theorem Proof sketch for Gödel's first incompleteness theorem Proof sketch for Gödel's first incompleteness theorem Proof sketch for Gödel's first incompleteness theorem
dbp:wikiPageUsesTemplate	dbt:= dbt:Math dbt:More_citations_needed dbt:Reflist dbt:Mathematical_logic
has abstract	Dieser Artikel skizziert Beweise der Gödelschen Unvollständigkeitssätze. Dabei handelt es sich um zwei mathematische Sätze, die zu den wichtigsten Ergebnissen der Logik gezählt werden und die von Kurt Gödel 1930 bewiesen wurden. Der erste Unvollständigkeitssatz besagt, dass kein konsistentes Axiomensystem, dessen Theoreme von einem Algorithmus aufgezählt werden können, alle wahren Aussagen über natürliche Zahlen mit Addition und Multiplikation beweisen kann. Der zweite Unvollständigkeitssatz besagt, dass ein solches System die eigene Widerspruchsfreiheit nicht beweisen kann. (de) This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses, which are discussed as needed during the sketch. We will assume for the remainder of the article that a fixed theory satisfying these hypotheses has been selected. Throughout this article the word "number" refers to a natural number. The key property these numbers possess is that any natural number can be obtained by starting with the number 0 and adding 1 a finite number of times. (en)
prov:wasDerivedFrom	wikipedia-en:Proof_sketch_for_Gödel's_first_incompleteness_theorem?oldid=1106008895&ns=0
page length (characters) of wiki page	22681 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Proof_sketch_for_Gödel's_first_incompleteness_theorem
is rdfs:seeAlso of	History of mathematical notation Gödel's incompleteness theorems
is Link from a Wikipage to another Wikipage of	Proof sketch for Godel's first incompleteness theorem Proof sketch for Goedel's first incompleteness theorem Truth Gödel numbering Ability
is Wikipage redirect of	Proof sketch for Godel's first incompleteness theorem Proof sketch for Goedel's first incompleteness theorem
is foaf:primaryTopic of	wikipedia-en:Proof_sketch_for_Gödel's_first_incompleteness_theorem

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