Transferring ideals

Monroe Eskew (U of Vienna)

Jun 28. 2024, 14:00 — 14:45

In recent work with Hayut, we produced a model where for all n > 0, there is a normal ideal $I$ on $\omega_n$ with $P(\omega_n)/I$ forcing equivalent to $Col(\omega_{n-1},\omega_n)$.  The most interesting consequences of this stem from a transfer theorem of Woodin that allows us to find copies of boolean algebas of the form $P(\omega_n)/I$ in ones of the form $P(\omega_m)/J$ for $m>n$ and with $J$ uniform and having the same additivity as $I$.  We will sketch the proof of Woodin's theorem, raise the question of whether some these transfers can be witnessed by certain surjections that give rise to a direct limit generic ultrapower, and discuss what this could mean for further combinatorial applications.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Determinacy, Inner Models and Forcing Axioms (Workshop)
Organizer(s):
Sandra Müller (TU Vienna)
Grigor Sargsyan (Polish Academy of Science, Warsaw)
Ralf Schindler (WWU Münster)
John Steel (UC, Berkeley)