HODs, mantles, strategy mice, and self-iterability
Basic data for this talk
Type of talk: scientific talk
Name der Vortragenden: Schlutzenberg, Farmer
Date of talk: 04/07/2019
Talk language: English
URL of slides: https://www.univie.ac.at/projektservice-mathematik/e/talks/Schlutzenberg_2019-07_V_om.pdf
Information about the event
Name of the event: Seventh European Set Theory Conference
Event period: 01/07/2019 - 05/07/2019
Event location: Wien, Österreich
Event website: https://sites.google.com/view/estc2019/
Abstract
Fine structural inner models come in two main forms: pure extender mice L[E], and extender/strategy mice L[E,Σ], where Σ codes a partial iteration strategy for the structure. We will discuss recent results analysing HODs and mantles associated to certain pure extender mice, in terms of strategy mice. This is analogous to the analysis of HODs of determinacy models. We thereby derive the existence of iterable strategy mice with Woodin cardinals from the existence of iterable pure extender mice with interleaved Woodin and strong cardinals, and establish that the extender mice in question compute a significant fragment of their own iteration strategy. The work is partly joint with G. Sargsyan and R. Schindler.Keywords: Set theory; inner model theory; large cardinal; fine structure; self-iterability; set theoretic geology; ordinal definability
Speakers from the University of Münster
| Schlutzenberg, Farmer | Junior professorship for mathematical logic (Prof. Schlutzenberg) |