会议名称：Set Theory Workshop

时间：2024年4月15日

地点：数学院南楼N219

会议主办方：中国科学院数学与系统科学研究院

会议组织者：彭银河；吴刘臻

会议日程：

9：30-10：30  报告人：Stevo Todorcevic

10：40-11：30 报告人：何家亮

14：00-14：50 报告人：肖鸣

15：00-15：50 报告人：袁嘉辰

16：00-16：50 报告人：David Schrittesser 

标题及摘要：

报告人：Stevo Todorcevic（University of Toronto）

标题：Frechet groups

摘要：The interaction between the topological and algebraic structure is particularly interesting in the case of Frechet groups, the groups in which closure of a set is obtained by taking the limits of sequences of elements  of the set.  We shall survey this area of research and list some of its open problem such as, for example, the  problem of existence of a Frechet group whose square is not Frechet.

报告人：何家亮（四川大学）

标题：An example of $\Sigma^0_3$ ideal of compact sets

摘要：Metheron and Zeleny asked if every $\Sigma^0_3$ ideal of compact sets expressible as a countable union of $G_\delta$ hereditary sets? In this talk, I will construct a counter-example for their question.

报告人：肖鸣（南开大学）

标题：Order analysis of hyperfinite Borel equivalence relations

摘要：It is well known that a countable Borel equivalence relation is hyperfinite if and only if there is a Borel way to assign to each class a linear order which is either finite or ismorphic to $\mathbb{Z}$. In this talk we study how such orders interact with each other. This is a joint work with Su Gao.

报告人：袁嘉辰（University of Leeds）

标题：What happens at the limit of a sequence of models of ZFC

摘要：The technique of taking the tail model is a understudied object in the study of Mathematical logic. With Assaf Rinot and Zhixing You, we find it is a useful tool for constructing interesting ultrafilters. In this talk, I'll illustrate how we use it to answer a question about $\delta$-complete ultrafilters and to extend some results in infinitary combinatorics.

报告人：David Schrittesser（哈尔滨工业大学）

标题：Generalizing de Finetti

摘要：Intuitively, de Finetti's theorem states that if we make a sequence of measurements in a setting where we know it to be irrelevant in which order these measurements are obtained, then these measurements are conditionally independent (independent given some latent random element). To be more precise, here is one version of de Finetti's theorem: Given a sequence of real random variables X1, X2, ... whose joint distribution is invariant under permutations of the indices, if we condition each Xi on the exchangeable algebra E obtaining the random variable (Xi | E), then the (Xi | E) are identically and independently distributed.

 It turns out that the assumption that the state space is "nice" (here, the real numbers) is crucial to this theorem. One can ask if this theorem holds for sequences of random elements whose state space is some more general measure space (that is, not just for sequences of real random variables). In this talk, I discuss this question. In particular, I give a characterization of conditionally iid sequences without any assumptions on the state space, as well as a version of de Finetti for sequences whose common distribution is Radon (strengthening a recent theorem due to Alam Irfan).

 This is joint work with Peter Potaptchik (Oxford) and Daniel M. Roy (University of Toronto).