Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Relative Consistency in Set Theory

Sean Cox
Wednesday, March 7, 2007
4:00 pm - 4:50 pm
MSTB 114

Talk Abstract:

The Zermelo-Fraenkel axioms with Choice (ZFC) are the standard axioms of set theory. Assuming ZFC is consistent, Gödel proved that there are statements which are independent of ZFC (the statement S is independent of ZFC if both (ZFC + S) and (ZFC + "not S") are consistent; equivalently, ZFC cannot prove either S or its negation). The Continuum Hypothesis (CH) turned out to be such a statement. Gödel showed CH is consistent with ZFC, and Cohen showed its negation is consistent with ZFC. I will give very rough sketches of these proofs. These sketches will introduce the main tools used to establish relative consistency between collections of axioms which extend ZFC. Finally, I will discuss large cardinals and my own research.

About the Speaker:

Sean Cox is a fifth-year Ph.D. student at UCI. He received his B.A. in economics from North Carolina State University (Raleigh) in 1999. His research involves locating the consistency strength (on the large cardinal scale) of various set-theoretic statements. He specializes in inner model theory, which is often used to find lower bounds for the consistency of such statements.

Refreshments:

Pizza will be served after the talk.