30 May 2014, 13:30–15:00

Fields institute, Room 210

Speaker: Asger Törnquist.

Title: Statements that are equivalent to CH and their Sigma-1-2 counterparts

Abstract: There is a large number of “peculiar” statements that have been shown over time to be equivalent to the Continuum Hypothesis, CH. For instance, a well-known theorem of Sierpinski says that CH is equivalent to the statement that the plane can be covered by countably many graphs of functions (countably many of which are functions of x, and countably many of which are functions of y.) What happens if we consider the natural Sigma-1-2 analogues of these statements (in the sense of descriptive set theory)? It turns out that then these statements are, in a surprising number of cases, equivalent to that all reals are constructible. In this talk I will give many examples of this phenomenon, and attempt to provide an explanation of why this occurs. This is joint work with William Weiss.