Institute of Information Science Academia Sinica
講 題: 應用邏輯討論會系列 (XL) - Categoricity spectra and effective classifications
講 者: Nikolay Bazhenov 教授 (俄羅斯科學院西伯利亞分院, 索博列夫數學研究所)
時 間: 2018-10-12 (Fri) 15:30 – 17:30
地 點: 資訊所新館106演講廳
邀請人: 廖純中
摘要:

The general area of effective algebra is devoted to studying the algorithmic content of mathematical structures. The standard model for such investigations is a (Turing) computable presentation of an algebraic structure. A computable structure S is computably categorical if for any computable presentation A of S, there is a Turing computable isomorphism from A onto S. The notion of categoricity spectrum, which is built upon computable categoricity, captures the complexity of isomorphisms between different computable presentations of a given structure. For a class of structures K, effective classification gives a measure of complexity for computably presentable members of K. In the talk, we give a review of recent results on categoricity spectra and related effective classification problems.