Bar-Ilan-Jerusalem Set Theory Seminar
Time: Wednesday, August 12, 11:00am Israel Time (10:00 CEST)
Speaker: Uri Abraham, Ben-Gurion University
Title: Coding well ordering of the reals with ladders, part 4
Abstract: Results from the 2002 paper “Coding with Ladders a Well Ordering of the Reals” by Abraham and Shelah.
Information: contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.
CUNY Logic Seminar (MOPA)
Time: Wednesday, August 12, 19:00 New York time (1:00am July 30 CEST) – note the time
Speaker: Athar Abdul-Quader Purchase College
Title: CP-genericity and neutrality
Abstract: In a paper with Kossak in 2018, we studied the notion of neutrality: a subset X of a model M of PA is called neutral if the definable closure relation in (M, X) coincides with that in M. This notion was suggested by Dolich. motivated by work by Chatzidakis-Pillay on generic expansions of theories. In this talk, we will look at a more direct translation of the Chatzidakis-Pillay notion of genericity, which we call ‘CP-genericity’, and discuss its relation to neutrality. The main result shows that for recursively saturated models, CP-generics are always neutral; previously we had known that not all neutral sets are CP-generic.
Information: The seminar will take place virtually. Please email Victoria Gitman (firstname.lastname@example.org) for the meeting id.
CUNY Set Theory Seminar
Time: Friday, August 14, 14:00 New York time (20:00 CEST)
Speaker: Gunter Fuchs CUNY
Title: Canonical fragments of the strong reflection principle
Abstract: I have been working over the past few years on the project of trying to improve our understanding of the forcing axiom for subcomplete forcing. The most compelling feature of this axiom is its consistency with the continuum hypothesis. On the other hand, it captures many of the major consequences of Martin’s Maximum. It is a compelling feature of Martin’s Maximum that many of its consequences filter through Todorcevic’s Strong Reflection Principle SRP. SRP has some consequences that the subcomplete forcing axiom does not have, like the failure of CH and the saturation of the nonstationary ideal. It has been unclear until recently whether there is a version of SRP that relates to the subcomplete forcing axiom as the full SRP relates to Martin’s Maximum, but it turned out that there is: I will detail how to associate in a canonical way to an arbitrary forcing class its corresponding fragment of SRP in such a way that (1) the forcing axiom for the forcing class implies its fragment of SRP, (2) the stationary set preserving fragment of SRP is the full principle SRP, and (3) the subcomplete fragment of SRP implies the major consequences of the subcomplete forcing axiom. I will describe how this association works, describe some hitherto unknown effects of (the subcomplete fragment of) SRP on mutual stationarity, and say a little more about the extent of (3).
Information: Please email Victoria Gitman (email@example.com) for meeting id (this talk will have a different meeting ID!).