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arXiv · 2207.02642

Extension of sectional pseudocomplementation in posets

Jānis Cīrulis
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Abstract

Sectional pseudocomplementation (sp-complementation) on a poset is a partial operation $*$ which associates with every pair $(x,y)$ of elements, where $x \ge y$, the pseudocomplement $x*y$ of $x$ in the upper section $[y)$. Any total extension $\to$ of $*$ is said to be an extended sp-complementation and is considered as an implication-like operation. Extended sp-complementations have already be studied on semilattices and lattices. We describe several naturally arising classes of general posets with extended sp-complementation, present respective elementary properties of this operation, demonstrate that two other known attempts to isolate particular such classes are in fact not quite correct, and suggest suitable improvements.

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Jānis Cīrulis. 2022-07-05. Extension of sectional pseudocomplementation in posets. https://arxiv.org/abs/2207.02642

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