Some applications of Supercompact Extender Based Forcings to HOD
Moti Gitik, Carmi Merimovich
TL;DR
This paper explores the use of supercompact extender based forcings to construct models where the HOD (Hereditarily Ordinal Definable sets) has a different cardinal structure from the universe, including models where all regular uncountable cardinals are measurable in HOD.
Contribution
It introduces new applications of supercompact extender based forcings to manipulate the HOD's cardinal structure, including making all regular uncountable cardinals measurable in HOD.
Findings
Constructed a model with all regular uncountable cardinals measurable in HOD.
Demonstrated the versatility of supercompact extender based forcings in controlling HOD properties.
Abstract
Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V. In particular, a model with all regular uncountable cardinals measurable in HOD is constructed.
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