Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A model-theoretic characterization of monadic second order logic on
  infinite words   Monadic second order logic and linear temporal logic are two logical
formalisms that can be used to describe classes of infinite words, i.e.,
first-order models based on the natural numbers with order, successor, and
finitely many unary predicate symbols.
  Monadic second order logic over infinite words (S1S) can alternatively be
described as a first-order logic interpreted in $\mathcal{P}(\omega)$, the
power set Boolean algebra of the natural numbers, equipped with modal operators
for 'initial', 'next' and 'future' states. We prove that the first-order theory
of this structure is the model companion of a class of algebras corresponding
to the appropriate version of linear temporal logic (LTL) without until.
  The proof makes crucial use of two classical, non-trivial results from the
literature, namely the completeness of LTL with respect to the natural numbers,
and the correspondence between S1S-formulas and B\"uchi automata.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph