Gödel's incompleteness theorems
GPTKB entity
Statements (25)
Predicate | Object |
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gptkbp:instanceOf |
gptkb:mathematical_concept
|
gptkbp:appliesTo |
gptkb:logic
gptkb:Peano_arithmetic formal systems |
gptkbp:category |
gptkb:logic
theoretical computer science |
gptkbp:countryOfPublication |
gptkb:German
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gptkbp:firstTheoremStates |
Any consistent formal system that is capable of expressing elementary arithmetic cannot be both complete and consistent.
|
gptkbp:formedBy |
gptkb:Kurt_Gödel
1931 |
https://www.w3.org/2000/01/rdf-schema#label |
Gödel's incompleteness theorems
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gptkbp:influenced |
gptkb:logic
computer science |
gptkbp:numberOfTheorems |
2
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gptkbp:publishedIn |
gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
gptkb:Monatshefte_für_Mathematik |
gptkbp:relatedTo |
gptkb:Hilbert's_program
gptkb:Turing's_halting_problem completeness undecidability consistency |
gptkbp:secondTheoremStates |
No consistent system can prove its own consistency.
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gptkbp:bfsParent |
gptkb:Hilbert's_program
gptkb:logic |
gptkbp:bfsLayer |
4
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