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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 Principles of Mathematical Logic ： ウィキペディア英語版 Principles of Mathematical Logic ''Principles of Mathematical Logic'' is the 1950〔 The translation of the 1938 2nd German edition into English was published in 1950, while the 3rd German edition was published in 1949.〕 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text ''Grundzüge der theoretischen Logik'', on elementary mathematical logic. The 1928 first edition thereof is considered the first elementary text clearly grounded in the formalism now known as first-order logic (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status. FOL is now a core formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory. The 1928 edition included a clear statement of the Entscheidungsproblem (decision problem) for FOL, and also asked whether that logic was complete (i.e., whether all semantic truths of FOL were theorems derivable from the FOL axioms and rules). The first problem was answered in the negative by Alonzo Church in 1936. The second was answered affirmatively by Kurt Gödel in 1929. The text also touched on set theory and relational algebra as ways of going beyond FOL. Contemporary notation for logic owes more to this text than it does to the notation of ''Principia Mathematica'', long popular in the English speaking world. ==Notes== 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「Principles of Mathematical Logic」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.