Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization theorem for geometric logic   We establish a criterion for deciding whether a class of structures is the
class of models of a geometric theory inside Grothendieck toposes; then we
specialize this result to obtain a characterization of the infinitary
first-order theories which are geometric in terms of their models in
Grothendieck toposes, solving a problem posed by Ieke Moerdijk in 1989.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin