Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sublattices of lattices of order-convex sets, III. The case of totally
  ordered sets   For a partially ordered set P, let Co(P) denote the lattice of all
order-convex subsets of P. For a positive integer n, we denote by SUB(LO)
(resp., SUB(n)) the class of all lattices that can be embedded into a product
of lattices of convex subsets of chains (resp., chains with at most n
elements). We prove the following results: (1) Both classes SUB(LO) and SUB(n),
for any positive integer n, are locally &#64257;nite, &#64257;nitely based
varieties of lattices, and we &#64257;nd &#64257;nite equational bases of these
varieties. (2) The variety SUB(LO) is the quasivariety join of all the
varieties SUB(n), for 1 &#8804; n < \omega, and it has only countably many
subvarieties. We classify these varieties, together with all the &#64257;nite
subdirectly irreducible members of SUB(LO). (3) Every &#64257;nite subdirectly
irreducible member of SUB(LO) is projective within SUB(LO), and every
subquasivariety of SUB(LO) is a variety.

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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: math-ph