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In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, 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 a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.

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rdf:type	Thing software
rdfs:label	Hilbert's program (en)
rdfs:comment	In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, 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 a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. (en)
sameAs	Hilbert's program Hilbert's program
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Subject	Proof theory Hilbert's problems Mathematical logic
gold:hypernym	Solution
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Hilbert's_program?oldid=1070549690&ns=0
Wikipage page ID	607286 (xsd:integer)
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Wikipage revision ID	1070549690 (xsd:integer)
Link from a Wikipage to another Wikipage	Formal language Foundations of mathematics Proof theory Algebraically closed field Analytic geometry Arithmetic Atomism Axiom Cantor–Dedekind axiom Proof theory Gentzen's consistency proof Gerhard Gentzen German diaspora Hilbert's problems Mathematical logic David Hilbert Kurt Gödel Zermelo–Fraenkel set theory Characteristic (algebra) Complete theory Consistency Ordinal number Reverse mathematics Entscheidungsproblem First-order logic Gaisi Takeuti Grundlagen der Mathematik Gödel's incompleteness theorems Peano axioms Transfinite induction Euclidean geometry Mathematical logic Mathematics Real analysis Richard Zach
has abstract	In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, 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 a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. In his first theorem, Gödel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete: it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. In his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore anything else. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Hilbert's_program
is rdfs:seeAlso of	John von Neumann
is Wikipage redirect of	Hilbert's Program Hilbert's programme Hilbert Program Hilbert program
is Link from a Wikipage to another Wikipage of	Formalism (philosophy of mathematics) Foundations of mathematics List of things named after David Hilbert Logic Arithmetization of analysis Carl Gustav Hempel Jacques Herbrand David Hilbert Differential geometry Hilbert space History of artificial intelligence History of logic Metamathematics Metatheory Certainty List of eponyms (A–K) List of mathematical logic topics Consistency Hilbert's Program Hilbert's problems Epsilon calculus Equiconsistency Finitism Index of philosophy articles (D–H) Hilbert's programme Hilbert Program Hilbert program Gödel's incompleteness theorems John von Neumann Mathematical logic Mathematics
is known for of	David Hilbert
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Hilbert's_program

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