Institute of Information Science Academia Sinica
Topic: Applied Logics Seminar Series(XL) -- Categoricity spectra and effective classifications
Speaker: Prof. Nikolay Bazhenov (Sobolev Institute of Mathematics, Russia )
Date: 2018-10-12 (Fri) 15:30 – 17:30
Location: Auditorium 106 at IIS new Building
Host: Churn-Jung Liau

Abstract:

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.