[logic-ml] JAIST Logic Seminar Series - Beckmann 教授講演のお知らせ (10月4日)

[Nao Hirokawa]

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)

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* 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.