Cichon’s maximum without large cardinals
Date/Time: July 26, 2019 (Friday) / 16:00 - 17:00
Speaker: Prof. Diego A. Mejía (Shizuoka Univ.)
Venue: Rm 1201, Science Complex A, Tohoku Univ.
Abstract: Cichon’s diagram is formed by cardinal characteristics of combinatorial properties related to Lebesgue measure, category and compactness of subsets of the irrationals. In the 1980’s decades it was proved that the diagram is complete (in the sense that no other inequality can be proved), but just very recently the search of models where many cardinals of the diagram can be pairwise different has been very active.
Jointly with Goldstern, Kellner and Shelah, we proved that all the cardinals in the diagram can be pairwise different (exlcuding, of course, obvious equalities). In this seminar I will outline the proof of this result. No deep understanding of forcing is required, instead the talked is supported on basic knowledge about models of set theory and elementary embeddings.