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Hilbert's program

In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to…

Hilbert's program after Gödel, Gödel's incompleteness theorems & Statement of Hilbert's program

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Statement of Hilbert's program

Gödel's incompleteness theorems

Hilbert's program after Gödel

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Hilbert's program

Nodes44
Edges43
Triples55
Avg. degree1.95
Density0.045455
Components1

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Hilbert's program

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related to References · 29
Hilbert's program → Die Grundlegung, Die Widerspruchfreiheit, Elementary Number Theory, Ewald, From Brouwer, Gentzen, Gerhard Gentzen, Hilbert, Hilbert's, Hilbert's Program Then, Journal, LO, Logic, Mancosu, Mathematische Annalen, New York, Now, Oxford University Press, Partial, Philosophy
related to Gödel's incompleteness theorems · 9
Hilbert's program → Entscheidungsproblem, Gödel's, Hilbert's, It, Kurt Gödel, Peano, Strictly, There, This
related to Statement of Hilbert's program · 8
Hilbert's program → Completeness, Conservation, Consistency, Decidability, Hilbert's, In, The, This
related to External links · 7
Hilbert's program → Edward, In Zalta, ISSN, OCLC, Philosophy, Richard Zach, Stanford Encyclopedia

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consistency mathematics arithmetic hilbert's program proof peano consistent theory set hilbert could cannot prove showed system statement axioms mathematical algorithm

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SubjectPredicateObjectConfidenceSrc
Peano arithmetic cannot even prove its own consistencyinstance ofconsistent extension of even Peano arithmetic based on a computably enumerable set of axioms.A theory0.80text
so a restrictedinstance ofconsistent extension of even Peano arithmetic based on a computably enumerable set of axioms.A theory0.80text
Hilbert's programrelated to External linksRichard Zach0.60section
Hilbert's programrelated to External linksIn Zalta0.60section
Hilbert's programrelated to External linksEdward0.60section
Hilbert's programrelated to External linksStanford Encyclopedia0.60section
Hilbert's programrelated to External linksPhilosophy0.60section
Hilbert's programrelated to External linksISSN0.60section
Hilbert's programrelated to External linksOCLC0.60section
Hilbert's programrelated to Gödel's incompleteness theoremsKurt Gödel0.60section
Hilbert's programrelated to Gödel's incompleteness theoremsHilbert's0.60section
Hilbert's programrelated to Gödel's incompleteness theoremsGödel's0.60section

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