Local club condensation in extender models
Seminar
Speaker
Gabriel Fernandes (BIU)
Date
22/10/2020 - 12:00 - 10:00Add to Calendar
2020-10-22 10:00:00
2020-10-22 12:00:00
Local club condensation in extender models
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^++).
zoom
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
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^++).
Last Updated Date : 15/10/2020
