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Leon Albert Henkin (19 April 1921, Brooklyn – 1 November 2006, Oakland, California)〔(UC Berkeley mathematics professor dies. ) Oroville Mercury-Register. November 24, 2006〕 was a logician at the University of California, Berkeley. He was principally known for the "Henkin's completeness proof": his version of the proof of the semantic completeness of standard systems of first-order logic. ==The completeness proof== Henkin's result was not novel; it had first been proved by Kurt Gödel in his doctoral dissertation, which was completed in 1929. (See Gödel's completeness theorem. Gödel published a version of the proof in 1930.) Henkin's 1949 proof is much easier to survey than Gödel's and has thus become the standard choice of completeness proof for presentation in introductory classes and texts. The proof is non-constructive, i.e. it is a pure existence proof. While it guarantees that if a sentence α follows (semantically) from a set of sentences Σ, then there ''is'' a proof of α from Σ, it gives no indication of the nature of that proof. Henkin originally proved the completeness of Church's higher-order logic, and then observed that the same methods of proof could be applied to first-order logic. Henkin's proof for higher-order logic uses a variant of the standard semantics. This variant uses general models (models in general or Henkin semantics; models in Henkin semantics are not to be confused with Henkin models, which are models in classical first-order logic): the higher types need not be interpreted by the full space of functions; a subset of the function space may be used instead. 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「Leon Henkin」の詳細全文を読む スポンサード リンク
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