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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hilbert–Bernays provability conditions ： ウィキペディア英語版 Hilbert–Bernays provability conditions In mathematical logic, the Hilbert–Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic (Smith 2007:224). These conditions are used in many proofs of Kurt Gödel's second incompleteness theorem. They are also closely related to axioms of provability logic. == The conditions == Let ''T'' be a formal theory of arithmetic with a formalized provability predicate Prov(''n''), which is expressed as a formula of ''T'' with one free number variable. For each formula φ in the theory, let #(φ) be the Gödel number of φ. The Hilbert–Bernays provability conditions are: # If ''T'' proves a sentence φ then ''T'' proves Prov(#(φ)). # For every sentence φ, ''T'' proves Prov(#(φ)) → Prov(#(Prov(#(φ)))) # ''T'' proves that Prov(#(φ → ψ)) and Prov(#(φ)) imply Prov (#(ψ)) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hilbert–Bernays provability conditions」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.