A Cayley theorem for posets

TL;DR

This paper proves that any poset satisfying the Ascending Chain Condition can be explicitly embedded into a poset of mappings from itself to its antichains, extending Cayley's theorem to posets.

Contribution

It introduces a Cayley-type theorem for posets satisfying the Ascending Chain Condition, providing an explicit isomorphic embedding.

Findings

Posets with ASC can be embedded into a poset of mappings to their antichains

Explicit construction of the isomorphism is provided

Extends Cayley's theorem to a new class of posets

Abstract

We show that every poset P=(P,\le) satisfying the Ascending Chain Condition can be isomorphically embedded into the poset of all mappings from P to the set A(P) of all antichains of P equipped with a certain partial order relation. This isomorphism is presented explicitly.