Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Keisler-Shelah isomorphism theorem and the continuum hypothesis II   We continue the investigation started in [Sh:1215] about the relation between
the Keilser-Shelah isomorphism theorem and the continuum hypothesis. In
particular, we show it is consistent that the continuum hypothesis fails and
for any given sequence $\mathbf m=\langle (\mathbb{M}^{1}_n, \mathbb{M}^{2}_n:
n < \omega \rangle$ of models of size at most $\aleph_1$ in a countable
language, if the sequence satisfies a mild extra property, then for every
non-principal ultrafilter $\mathcal D$ on $\omega$, if the ultraproducts
$\prod\limits_{\mathcal D} \mathbb{M}^{1}_n$ and $\prod\limits_{\mathcal D}
\mathbb{M}^{2}_n$ are elementarily equivalent, then they are isomorphic.

27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex