### On supercompactness of omega_1

Logic and Set Theory Seminar

20th August 2019, 1:30 pm – 3:00 pm

Howard House, 4th Floor Seminar Room

In ZFC, all the large cardinals are much bigger than \omega_1, the least uncountable cardinal. In ZF without assuming the Axiom of Choice, \omega_1 could have large cardinal properties such as measurability and supercompactness by the results of Jech and Takeuti. In this talk, we discuss some consequences of supercompactness of \omega_1 on sets of reals in terms of regularity properties and determinacy. This is joint work with Nam Trang.

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