Bar-Ilan-Jerusalem Set Theory Seminar
Time: Wednesday, August 5, 11:00am Israel Time (10:00 CEST)
Speaker: Uri Abraham, Ben-Gurion University
Title: Coding well ordering of the reals with ladders, part 3
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 Set Theory Seminar
Time: Friday, August 7, 14:00 New York time (20:00 CEST)
Speaker: Brent Cody, Virginia Commonwealth University
Title: Higher indescribability
Abstract: To what extent can formulas from infinitary logics be used in set-theoretic reflection arguments? If κ is a measurable cardinal, any Lκ,κ sentence which is true in (κ,∈), must be true about some strictly smaller cardinal. Whereas, there are Lκ+,κ+ sentences of length κ which are true in (κ,∈)and which are not true about any smaller cardinal. However, if κ is a measurable cardinal and some Lκ+,κ+ sentence φ is true in (κ,∈), then there must be some strictly smaller cardinal α<κsuch that a canonically restricted version of φ holds about α. Building on work of Bagaria and Sharpe-Welch, we use canonical restriction of formulas to define notions of Π1ξ-indescribability of a cardinal κ for all ξ<κ+. In this context we show that such higher indescribability hypotheses are strictly weaker than measurability, we prove the existence of universal Π1ξ-formulas, study the associated normal ideals and notions of ξ-clubs and prove a hierarchy result. Time permitting we will discuss some applications.
Information: Please email Victoria Gitman (firstname.lastname@example.org) for meeting id (this talk will have a different meeting ID!).