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Results tagged with posets
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user 46855
A poset or partially ordered set is a set endowed with a partial order, meaning a binary relation $\leq$ which is reflexive ($x \leq x$ for all $x$), antisymmetric ($x\leq y$ and $y\leq x$ implies $x=y$), and transitive ($x\leq y$ and $y\leq z$ implies $x \leq z$).
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Minimal (semi)lattice containing a given poset
it sufficies to see that one isotone map from $P$ to a $L$ is injective, and this follows from Birkhoff transform (embedding of $P$ in its lattice of order ideals, i.e. categorical equivalence between posets … For a poset $P$, you essentially consider the class of all posets $Q$ that have $P$ as sub-poset, and the following preorder: $Q\preceq Q'$ iff there is a poset embedding of $Q$ in $Q'$ that fixes each …
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