Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a Ryll-Nardzewski-type Theorem for weakly oligomorphic
  structures   A structure is called weakly oligomorphic if it realizes only finitely many
n-ary positive existential types for every n. The goal of this paper is to show
that the notions of homomorphism-homogeneity, and weak oligomorphy are not only
completely analogous to the classical notions of ultrahomogeneity and
oligomorphy, but are actually closely related. A first result is a
Fra\"iss\'e-type theorem for homomorphism-homogeneous relational structures.
Further we show that every weakly oligomorphic homomorphism-homogeneous
structure contains (up to isomorphism) a unique homogeneous,
homomorphism-homogeneous core, to which it is homomorphism-equivalent. As a
consequence, we obtain that every countable weakly oligomorphic structure is
homomorphism-equivalent with a finite or \omega-categorical structure. Another
result is the characterization of positive existential theories of weakly
oligomorphic structures as the positive existential parts of \omega-categorical
theories. Finally, we show, that the countable models of countable weakly
oligomorphic structures are mutually homomorphism-equivalent (we call first
order theories with this property weakly \omega-categorical). These results are
in analogy with part of the Engeler-Ryll-Nardzewski-Svenonius-theorem.

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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn