Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pathological examples of structures with o-minimal open core   This paper answers several open questions around structures with o-minimal
open core. We construct an expansion of an o-minimal structure $\mathcal{R}$ by
a unary predicate such that its open core is a proper o-minimal expansion of
$\mathcal{R}$. We give an example of a structure that has an o-minimal open
core and the exchange property, yet defines a function whose graph is dense.
Finally, we produce an example of a structure that has an o-minimal open core
and definable Skolem functions, but is not o-minimal.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat