[logic-ml] 基礎論セミナー

[arai toshiyasu]

みなさま

直前になりましたが、第2回の基礎論セミナー
のお知らせです。
どなたでも聴講できますので
ご興味のおありの方はどうぞいらして下さい。

web page:
https://www.ms.u-tokyo.ac.jp/seminar/logic/

新井敏康

第2回基礎論セミナー
日時：2019年11月21日（木）13:30-15:00
場所：東京大学大学院数理科学研究科 003号室

講演者：佐藤憲太郎
title:
Self-referential Theorems for Finitist Arithmetic

abstract::
The finitist logic excludes,on the syntax level, unbounded quantifiers
and accommodates only bounded quantifiers.
The following two self-referential theorems for arithmetic theories
over the finitist logic will be considered:
Tarski's impossibility of naive truth predicate and
Goedel's incompleteness theorem.
Particularly, it will be briefly explained that
(i) the naive truth theory over the finitist arithmetic with summation
and multiplication
is consistent and proves its own consistency, and that
(ii) by the use of finitist arithmetic, the hierarchy of consistency strengths,
based on Goedel's second incompleteness theorem,
can be extended downward (to the area not reachable by first order
predicate arithmetic).
This is a joint work with Jan Walker, and overlaps significantly with
his doctoral dissertation.

問合せ先：新井敏康
tosarai at ms.u-tokyo.ac.jp