Online seminar series on logical and philosophical foundations of mathematics

报告题目: How many real numbers are there?

报告人: Prof. Ralf Schindler (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 ℵ₂ many real numbers: Forcing axioms and the P_max axiom (*), 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:

Ralf Schindler is a full professor in the department of mathematics and computer science at University of Muenster, and was the vice chair of the department. He was also Guest professor at UC Berkeley and the University of Barcelona. He was the co-editor of the Journal of Symbolic Logic and is the Editor-in-chief of the Archive for Mathematical Logic. He is the secretary of the European Set Theory Society and has served in various committees of international conferences and workshops.

Ralf Schindler is an expert in set theory. His research interest in set theory includes inner 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_max axiom (*), 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

武汉大学哲学学院