Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reversibility of Extreme Relational Structures   A relational structure $\mathbb{X}$ is called reversible iff each bijective
homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear
orders are prototypical examples of such structures. One way to detect new
reversible structures of a given relational language $L$ is to notice that the
maximal or minimal elements of isomorphism-invariant sets of interpretations of
the language $L$ on a fixed domain $X$ determine reversible structures. We
isolate certain syntactical conditions providing that a consistent $L_{\infty
\omega }$-theory defines a class of interpretations having extreme elements on
a fixed domain and detect several classes of reversible structures. In
particular, we characterize the reversible countable ultrahomogeneous graphs.

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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom