Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: HOD, V and the GCH   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 $HOD$.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess