Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal homogeneous constraint structures and the hom-equivalence
  classes of weakly oligomorphic structures   We derive a new sufficient condition for the existence of
{\omega}-categorical universal structures in classes of relational structures
with constraints, augmenting results by Cherlin, Shelah, Chi, and Hubi\v{c}ka
and Ne\v{s}et\v{r}il. Using this result we show that the hom-equivalence class
of any countable weakly oligomorphic structure has up to isomorphism a unique
model-complete smallest and greatest element, both of which are
{\omega}-categorical. As the main tool we introduce the category of constraint
structures, show the existence of universal homogeneous objects, and study
their automorphism groups. All constructions rest on a category-theoretic
version of Fra\"iss\'e's Theorem due to Droste and G\"obel. We derive
sufficient conditions for a comma category to contain a universal homogeneous
object. This research is motivated by the observation that all countable models
of the theory of a weakly oligomorphic structure are hom-equivalent---a result
akin to (part of) the Ryll-Nardzewski Theorem.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex