Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 7 October 2015, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Dilip Raghavan
Title: Real games and strategically selective coideals, Part 2.
A classical theorem of Mathias says that the Axiom of Determinacy for
Real games (AD_R) implies that there are no tall selective coideals on
omega. Farah introduced the notion of a semiselective coideal and
proved in ZF that these are precisely those ideals on omega whose
quotient adds a selective ultrafilter. It is unkown whether AD_R
implies the non-existence of tall semiselective coideals. We introduce
the notion of strategically selective coideal, and show that tall
strategically selective coideals do not exist under AD_R. The Axiom of
Choice implies that the notions of semiselective and strategically
selective coideal coincide.
This talk is a continuation of the talk from 16/09/2015 and will
provide more mathematical details and selected proofs.
This is joint work with Paul Larson.