Set Theory Seminar: Dominik Adolf (HUJI) - Scales in inner models

Wed, 07/07/202114:00-16:00

Dominik Adolf will talk about
 Scales in inner models.

Abstract: Tree like scales were introduced by Pereira in his PhD thesis. Unlike other properties like goodness, tree-likeness is known to be consistent with the existence of extremely strong large cardinals like I_0 -cardinals (Pereira) and supercompact cardinals (Cummings).
We will add to this by showing that tree-like scales also exist in all canonical (short extender) inner models. In fact, every product in such a model carries a continuous tree-like scale. If time permits we will also discuss when such scales exist in arbitrary universes by the use of core model theory

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