みなさま
第3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.