Dilip Raghavan: Real games and strategically selective coideals

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 16 September 2015, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Dilip Raghavan

Title: Real games and strategically selective coideals

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Joint Work with Paul Larson

Abstract: 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.

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