Incompactness of the second uncountable cardinal

Seminar
Speaker
Assaf Rinot (BIU)
Date
03/08/2021 - 16:00 - 14:00Add to Calendar 2021-08-03 14:00:00 2021-08-03 16:00:00 Incompactness of the second uncountable cardinal In a celebrated paper from 1997, Shelah proved that Pr1(w2,w2,w2,w) is a theorem of ZFC, and it remains open ever since whether moreover Pr1(w2,w2,w2,w1) holds. In an unpublished note from 2017, Todorcevic proved that a certain weakening of the latter follows from CH. In a recent paper with Zhang (arXiv:2104.15031), we gave a few weak sufficient conditions for Pr1(w2,w2,w2,w1) to hold. In an even more recent paper (arXiv:1910.02419v2), Shelah proved that it holds, assuming the existence of a nonreflecting stationary subset of S^2_0, hence, the strength of the failure is at least that of a Mahlo cardinal. In this talk, we'll prove that (weak forms of) square(w2) are sufficient for Pr1(w2,w2,w2,w1) to hold, thus raising the strength of the failure to that of a weakly compact cardinal. This is joint work with Jing Zhang.   Seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Seminar room
Abstract

In a celebrated paper from 1997, Shelah proved that Pr1(w2,w2,w2,w) is a theorem of ZFC, and it remains open ever since whether moreover Pr1(w2,w2,w2,w1) holds.

In an unpublished note from 2017, Todorcevic proved that a certain weakening of the latter follows from CH.
In a recent paper with Zhang (arXiv:2104.15031), we gave a few weak sufficient conditions for Pr1(w2,w2,w2,w1) to hold.
In an even more recent paper (arXiv:1910.02419v2), Shelah proved that it holds, assuming the existence of a nonreflecting stationary subset of S^2_0, hence, the strength of the failure is at least that of a Mahlo cardinal.
In this talk, we'll prove that (weak forms of) square(w2) are sufficient for Pr1(w2,w2,w2,w1) to hold, thus raising the strength of the failure to that of a weakly compact cardinal.

This is joint work with Jing Zhang.
 

Last Updated Date : 27/07/2021