Polish groups with ample generics and analytic P-ideals

Speaker(s)

Maciej Malicki

Affiliation

Warsaw School of Economics

Date

Oct. 7, 2015, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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A Polish group has ample generics if all its diagonal conjugation actions have a comeager orbit. This property has a number of interesting implications, e.g. automatic continuity of homomorphisms into separable groups. Until recently, all known examples of Polish groups with ample generics were non-archimedean, i.e. they were isomorphic to automorphism groups of countable models. I will present a family of Polish groups with ample generics that are not of this form. Their construction uses analytic P-ideals.

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