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Hilbert's second problem

One of twenty-three, asking to prove the consistency of arithmetic axioms

In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions.

Nº Q13424667 ★

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Hilbert's second problem

One of twenty-three, asking to prove the consistency of arithmetic axioms

Texte en anglais

In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions.

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Texte en anglais Pas encore d'article dans ta langue : extrait en anglais.

In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions. Hilbert stated that the axioms he considered for arithmetic were the ones given in Hilbert (1900), which include a second order completeness axiom. In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that Gödel's theorems give a negative solution to the problem, while others consider Gentzen's proof as a partial positive solution.

Texte : Wikipédia en anglais, CC BY-SA 4.0. ·

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