HOD, V and the GCH
classification
🧮 math.LO
keywords
cardinalseverywherefailslargemodelanswersconstructexistence
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Starting from large cardinals we construct a model of $ZFC$ in which the $GCH$ fails everywhere, but such that $GCH$ holds in its $HOD$. The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we produce a model of $ZFC+GCH$ such that $GCH$ fails everywhere in its $HOD$.
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