Year: 2025
Type: article
Abstract: Based on earlier work of the third author, we construct a Chang-type model with supercompact measures extending a derived model of a given hod mouse with a regular cardinal [Formula: see text] that is both a limit of Woodin cardinals and a limit of [Formula: see text]-strong cardinals. The existence of such a hod mouse is consistent relative to a Woodin cardinal that is a limit of Woodin cardinals. We argue that our Chang-type model satisfies [Formula: see text] is regular + [Formula: see text] is [Formula: see text]-supercompact for some regular cardinal [Formula: see text]. This complements Woodin’s generalized Chang model, which satisfies [Formula: see text] is supercompact, assuming a proper class of Woodin cardinals that are limits of Woodin cardinals.
Source: Journal of Mathematical Logic
Authors: Takehiko Gappo, Sandra Müller, Grigor Sargsyan
Institutions: TU Wien, Institute of Mathematics, Polish Academy of Sciences
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408074403