[logic-ml] 基礎論セミナー

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みなさま

第3回の基礎論セミナーのお知らせです。
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web page:
https://www.ms.u-tokyo.ac.jp/seminar/logic/

新井敏康

第3回基礎論セミナー
日時：2019年12月20日（金）13:00-14:30
場所：東京大学大学院数理科学研究科 156号室

講演者：池上 大祐
title:
On supercompactness of \omega_1

abstract::
In ZFC, all the large cardinals are much bigger than \omega_1, the
least uncountable cardinal, while without assuming the Axiom of
Choice, \omega_1 could have some large cardinal properties. Jech and
Takeuti independently proved that if the axiom system ZFC + There is a
measurable cardinal is consistent, then so is ZF + \omega_1 is a
measurable cardinal. Takeuti also proved that one can replace
"measurable cardinal" above with "supercompact cardinal" as well as
some other large cardinals. Woodin proved that one can reduce the
assumption, i.e., the consistency of ZFC + a supercompact cardinal, to
that of ZFC + There are proper class many Woodin cardinals which are
limits of Woodin cardinals, to obtain the consistency of ZF + \omega_1
is a supercompact cardinal. Furthermore, the model he constructed also
satisfies the Axiom of Determinacy (AD).
In this talk, after giving some background on the connections between
large cardinals and determinacy, we discuss some consequences of the
axiom system ZF + \omega_1 is a supercompact cardinal. This is joint
work with Nam Trang.