Local club condensation in extender models

שלחו לחבר
Seminar
Speaker
Gabriel Fernandes (BIU)
Date
22/10/2020 - 12:00 - 10:00
Place
zoom
Abstract

Local club condensation is an abstraction of the condensation properties of the constructible hierarchy.
We will prove that for extender models that are countably iterable, given a cardinal kappa, the J_alpha^{E} hierarchy witnesses local club condensation in the interval (kappa^+,kappa^++) if and only if kappa is not a subcompact cardinal in L[E]. 

From the above and the equivalence between subcompact cardinals and square, due to Schimmerling and Zeman, it follows that in such extender models \square_kappa holds iff the J_alpha^{E} hierarchy witnesses that local club condensation holds in the interval (kappa^+,kappa^++).