数理逻辑系列报告

时间：2019.05.08（星期三）

地点：数学院南楼 N820 室

9:00-9:30 丁龙云教授（南开大学） 
题目：Abelian non-archimedean Polish groups and their actions
摘要：We investigate abelian Polish groups with a neighborhood basis of the identity consisting of open subgroups. A Polish group is called tame if all orbit equivalence relations of its Borel actions are Borel. We show that an abelian non-archimedean group G is tame iff any closed subgroup of G can homomorphically mapping onto neither Zω nor (⊕ω Z(p))ω for any prime p. We also consider the complexity of the orbit equivalence relation induced by a universal Borel action of any abelian non-archimedean group with respect to Borel reduction. This is a joint work with Su Gao.

9:40-10:10 郝兆宽教授（复旦大学） 
题目：Truth and Consistency in Set Theory 
摘要：In “The Hyperuniverse Program”, Sy-David Friedman claimed that PD, the projective determinacy, is consistent but not true. On the other hand, Hugh Woodin insists that the only reason that PD is consistent is that it is true. These two different positions lead to a philosophical problem of mathematics: in what case could we say a set theoretic sentence is true? In this talk we will discuss several possible positions toward answers of this problem, and try to argue that only Godel and Woodin’s strong Platonism is the coherent one.

10:20-10:50 喻良教授（南京大学）
题目：A recursion theoretical of a theorem of Banach
摘要：A function is called having Luzin (N) property if it sends every null set to a null set. In 1927, Banach proved that if a continuous function f has Luzin (N) property, then for almost every x, f？1({x}) iscountable. We provide a recursion theoretical proof of the result by applying the recent development of higher randomness theory. Some generalization of the result will also be considered.

11:00-11:30 张树果教授（四川大学） 
题目：Some Notes on Forcing 
摘要：We will talk about somthings about the relationships between the size of poset and certain kind of reals.