TL;DR
This paper constructs models of ZFC set theory with large cardinals where the GCH fails everywhere but holds in the HOD, answering a question by Sy Friedman and exploring the relationship between GCH and HOD.
Contribution
It introduces new models of ZFC with large cardinals where GCH behavior differs between the universe and HOD, addressing a specific open question.
Findings
GCH fails everywhere in the universe but holds in HOD in the constructed model
Models with large cardinals can have different GCH status in universe and HOD
Answers a question posed by Sy Friedman about GCH and HOD
Abstract
Starting from large cardinals we construct a model of in which the fails everywhere, but such that holds in its . The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we produce a model of such that fails everywhere in its .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis