西溪逻辑论坛第114期
Date: 8 May 2019 (15:00-17:00)
Venue: Room 259, Main Teaching Building, Xixi Campus, Zhejiang University
Speaker: Dr. Zachiri McKenzie (Shanghai Jiaotong University)
Title: Comparing foundational theories of mathematics and understanding subsystems of ZFC
Abstract:
I will begin by briefly describing several alternative approaches to the foundations of mathematics and different ways these theories can be compared. Subsystems and extensions of Zermelo-Fraenkel Set Theory with Choice (ZFC) play a particularly important role among these alternative foundations because of their diversity and the fruitful techniques, such as inner model theory and forcing, that have been developed in these theories. In this talk I will focus on subsystems ZFC. I will describe some commonly encounter subsystems of ZFC and their significance to alternative foundations of mathematics. I will discuss the importance of understanding the structure of nonstandard models of these theories and recent progress that has been made towards this understanding. I hope to draw your attention to some open questions in this area and future directions of research.  

(Supported by the Fundamental Research Funds for the Central Universities)