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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 Systems of Logic Based on Ordinals ： ウィキペディア英語版 Systems of Logic Based on Ordinals ''Systems of Logic Based on Ordinals'' was the PhD dissertation of the mathematician Alan Turing. The thesis is an exploration of formal mathematical systems after Gödel's theorem. Gödel showed for that any formal system S powerful enough to represent arithmetic, there is a theorem G which is true but the system is unable to prove. G could be added as an additional axiom to the system in place of a proof. However this would create a new system S' with its own unprovable true theorem G', and so on. Turing's thesis considers iterating the process to infinity, creating a system with an infinite set of axioms. The thesis was completed at Princeton under Alonzo Church and was a classic work in mathematics which introduced the concept of ordinal logic.〔Solomon Feferman, ''Turing in the Land of O(z)'' in "The universal Turing machine: a half-century survey" by Rolf Herken 1995 ISBN 3-211-82637-8 page 111〕 Martin Davis states that although Turing's use of a computing oracle is not a major focus of the dissertation, it has proven to be highly influential in theoretical computer science, e.g. in the polynomial time hierarchy.〔Martin Davis "Computability, Computation and the Real World", in ''Imagination and Rigor'' edited by Settimo Termini 2006 ISBN 88-470-0320-2 pages 63-66 ()〕 ==References== 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「Systems of Logic Based on Ordinals」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.