# Secil Tokgoz: OCA and Menger’s Conjecture

Place: Bahen Centre (Room BA2135)

Date: August 19th , 2016 (13:30-15:00)

Speaker: Secil Tokgoz

Title: OCA and Menger’s Conjecture

Abstract: It was previously known that Projective Determinacy implies Menger projective sets of reals are sigma-compact. The hypothesis has considerable large cardinal strength; we are able to reduce the conclusion’s consistency strength to that of an inaccessible. In fact this is an equiconsistency result. We derive the conclusion from a perfect strengthening of OCA. Equiconsistency is proved by an argument involving the dominating number and the Covering Lemma. This is joint work by Secil Tokgoz, Frank Tall and S. Todorcevic.