Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the abstract chromatic number and its computability for finitely
  axiomatizable theories   The celebrated Erd\H{o}s--Stone--Simonovits theorem characterizes the
asymptotic maximum edge density in $\mathcal{F}$-free graphs as $1 -
1/(\chi(\mathcal{F})-1) + o(1)$, where $\chi(\mathcal{F})$ is the minimum
chromatic number of a graph in $\mathcal{F}$. In Examples 25 and 31 of [L. N.
Coregliano and A. A. Razborov. Semantic limits of dense combinatorial objects.
Uspekhi Mat. Nauk, 75(4(454)):45-152, 2020], it was shown that this result can
be extended to the general setting of graphs with extra structure: the maximum
asymptotic density of a graph with extra structure without some induced
subgraphs is $1 - 1/(\chi(I) - 1) + o(1)$ for an appropriately defined abstract
chromatic number $\chi(I)$. As the name suggests, the original formula for the
abstract chromatic number is so abstract that its (algorithmic) computability
was left open.
  In this paper, we both extend this result to characterize maximum asymptotic
density of $t$-cliques in of graphs with extra structure without some induced
subgraphs in terms of $\chi(I)$ and we present a more concrete formula for
$\chi(I)$ that allows us to show its computability when both the extra
structure and the forbidden subgraphs can be described by a finitely
axiomatizable universal first-order theory. Our alternative formula for
$\chi(I)$ makes use of a partite version of Ramsey's Theorem for structures on
first-order relational languages.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys