Online seminar series on logical and philosophical foundations of mathematics

报告题目:How many real numbers are there?

报告人:Prof.RalfSchindler(University of Muenster, Germany)

时间:2020-12-08, 4pm-6pm

平台：ZOOM（ID：655 7906 2464）

Abstract:

Georg Cantor showed that there are uncountably many real numbers. But how many of them are there? Two sets of axioms have been intensively studied over the last 30 years which both imply that there are exactly ℵ₂many real numbers: Forcing axioms and the P_maxaxiom (*), but until recently they seemed to be competitors. Both of them encapsulate the idea that the universe of sets is rich or "saturated" in a precise way. Last year, David Asperó and myself verified that forcing axioms and (*) are actually compatible, a fact that might support the view that the right axiom to decide how many real numbers there are has already been found.

About the speaker:

RalfSchindleris a full professor in thedepartmentof mathematicsand computer scienceatUniversity of Muenster, and wasthe vice chair of the department.He wasalsoGuest professor at UC Berkeley and the University of Barcelona.He was theco-editor of the Journal of Symbolic Logicand is theEditor-in-chief of the Archive for Mathematical Logic.Heis thesecretaryofthe European Set Theory Societyand hasserved in various committees ofinternational conferences and workshops.

RalfSchindlerisan expert in set theory. Hisresearch interest inset theoryincludesinner model theory, large cardinals, descriptive set theory, and forcing axioms.He has made many contributions in set theory.Last year, together with David Asperó he answered a long standing open question in pure set theory by showing that Martin's Maximum⁺⁺implies Woodin's P_maxaxiom (*), which has strong impact on Cantor's Continuum Problem which asks how many real numbers there are.

主持人：程勇（武汉大学）

评论人:

冯 琦 (中国科学院数学与系统科学研究院)

吴刘臻 （中国科学院数学与系统科学研究院）

申国桢（武汉大学）

主办单位：

国家天元数学中部中心

武汉大学数学与统计学院

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