On monoids of isotone mappings

L. A. Skornyakov

Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 47-65

Résumé

The author introduces a class $\mathfrak D$ of sufficient monoids which are monoids isomorphic to certain special submonoids of monoids of isotone selfmaps of partially ordered sets with a greatest or least element. In contradistinction to the class of monoids isomorphic to monoids of all isotone maps, $\mathfrak D$ is an axiomatizable class. It follows from the isomorphism [elementary equivalence] of sufficient monoids of partially ordered sets $P$ and $P'$ that $P'$ is isomorphic [elementarily equivalent] to either $P$ or $P^{\mathrm{op}}$. Elementarily equivalent partially ordered sets possess elementarily equivalent sufficient monoids. Figures: 2. Bibliography: 19 titles.

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