All uncountable regular cardinals can be inaccessible in HOD
Mohammad Golshani
TL;DR
This paper demonstrates, under certain large cardinal assumptions, the construction of a model where all uncountable regular cardinals are inaccessible within HOD, advancing understanding of inner model theory.
Contribution
It shows the consistency of all uncountable regular cardinals being inaccessible in HOD assuming a supercompact and an inaccessible cardinal.
Findings
All uncountable regular cardinals are inaccessible in HOD in the constructed model.
The result relies on large cardinal assumptions.
It advances the understanding of the structure of HOD and large cardinal hypotheses.
Abstract
Assuming the existence of a supercompact cardinal and an inaccessible above it, we construct a model of ZFC, in which all uncountable regular cardinals are inaccessible in HOD.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Computability, Logic, AI Algorithms