Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modal logics of finite direct powers of $\omega$ have the finite model
  property   Let $(\omega^n,\preceq)$ be the direct power of $n$ instances of
$(\omega,\leq)$, natural numbers with the standard ordering, $(\omega^n,\prec)$
the direct power of $n$ instances of $(\omega,<)$. We show that for all finite
$n$, the modal logics of $(\omega^n,\preceq)$ and of $(\omega^n,\prec)$ have
the finite model property and moreover, the modal algebras of the frames
$(\omega^n,\preceq)$ and $(\omega^n,\prec)$ are locally finite.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph