Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal small extensions of o-minimal structures   A proper elementary extension of a model is called small if it realizes no
new types over any finite set in the base model. We answer a question of
Marker, and show that it is possible to have an o-minimal structure with a
maximal small extension. Our construction yields such a structure for any
cardinality. We show that in some cases, notably when the base structure is
countable, the maximal small extension has maximal possible cardinality.

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex