Set Theory Seminar: Shaun Allison (HUJI) - Polish groups with the pinned property, Part II

Wed, 18/05/202214:00-16:00
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Shaun will continue his talk from last week

Polish groups with the pinned property

 We will discuss a property of Polish groups called the "pinned property" which means that every orbit equivalence relation they generate is "pinned", a metamathematical notion which is used to separate the complexity of different equivalence relations up to Borel reducibility. We will discuss the subtle way that the amount of choice assumed influences the pinned property. In particular, we will discuss results of Su Gao and Alex Thompson which imply that in a mode of ZFC, a Polish group has the pinned property if and only if it has a complete compatible left-invariant metric. We will also present a new result which, along with a result of Larson-Zapletal, implies that in the Solovay model derived from a measurable, a Polish group has the pinned property if and only if it involves S_\infty (caveat: for the special case of non-Archimedian groups). Time permitting, we will discuss Larson-Zapletal's result as well. This is part of a larger project to measure and categorize the "classification strength" of Polish groups.

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Meeting ID: 816 7272 4380
Passcode: 998395