$\downarrow$-posets

Lawrence Valby

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arXiv · 1609.04440

$\downarrow$-posets

Lawrence Valby

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Abstract

We investigate a certain class of posets arising from semilattice actions. Let $S$ be a semilattice with identity. Let $S$ act on a set $C$. For $c,d\in C$ put $c\leq d$ iff there is some $s\in S$ with $ds=c$. Then $(C,\leq)$ is a poset. Let's call the posets that arise in this way $\downarrow$-posets. We give a reasonable second order characterization of $\downarrow$-posets and show that there is no first order characterization.

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BibTeX RIS

Lawrence Valby. 2016-09-14. $\downarrow$-posets. https://arxiv.org/abs/1609.04440

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