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  2. Hilbert's second problem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_second_problem

    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.

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