Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete $\mathcal{L}_{\omega_1,\omega}$-Sentences with Maximal Models
  in Multiple Cardinalities   In [BKS15] examples of incomplete sentences are given with maximal models in
more than one cardinality. The question was raised whether one can find similar
examples of complete sentences.
  In this paper we give examples of complete $L_{\omega_1,\omega}$-sentences
with maximal models in more than one cardinality. From (homogeneous)
characterizability of $\kappa$ we construct sentences with maximal models in
$\kappa$ and in one of $\kappa^+, \kappa^\omega, 2^\kappa$ and more. Indeed,
consistently we find sentences with maximal models in uncountably many distinct
cardinalities.

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The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org