皆様
１０月４日（金）に北陸先端科学技術大学院大学で行われます Arnold Beckmann 教授の講演のお知らせです。 皆様、どうぞ奮ってご参加ください。
廣川 直 (JAIST)
----------------------------------------------------------------------- * JAIST Logic Seminar Series *
Date: October 4 (Fri), 2019, 15:00 - 16:30
Place: I-65 (seminar room on 6F of IS Building III) at JAIST (Access: http://www.jaist.ac.jp/english/location/access.html)
Speaker: Arnold Beckmann (Swansea University)
Title: Consistency of equational theories and the separation problem for bounded arithmetic
Abstract: Consistency statements of formal theories have been considered as candidates for separating theories of bounded arithmetic. The most promising ones are given by consistency statements of certain equational theories. The starting points for this line of research are results by Buss and Ignjatovic 1995 [Unprovability of consistency statements in fragments of bounded arithmetic, APAL 1995, 74: 221--244], which shows that the consistency of an induction free version of the equational theory PV is not provable in the bounded arithmetic theory S^1_2, and Beckmann 2002 [Proving consistency of equational theories in bounded arithmetic. JSL 2002, 67: 279--296] which shows that the consistency of a further restricted induction free version of PV is provable in S^1_2.
We review those results and in particular state them precisely. We then explain the progress that has been made over recent years to narrow the gap between provability and unprovability, and the potential research programme that is related to this question.