Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The ordered set of principal congruences of a countable lattice   For a lattice L, let Princ L denote the ordered set of principal congruences
of L. In a pioneering paper, G. Gratzer characterized the ordered sets Princ L
of finite lattices L; here we do the same for countable lattices. He also
showed that each bounded ordered set H is isomorphic to Princ L of a bounded
lattice L. We prove a related statement: if an ordered set H with least element
is the union of a chain of principal order ideals, then H is isomorphic to
Princ L of some lattice L.

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th