A Cayley theorem for posets

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.

💡 Research Summary

The paper presents a Cayley‑type representation theorem for partially ordered sets (posets) that satisfy the Ascending Chain Condition (ACC). The classical Cayley theorem states that every group can be embedded into the symmetric group on its underlying set. Analogous results have been obtained for various algebraic structures (lattice‑ordered groups, Boolean algebras, Stone algebras, etc.). This work extends the idea to posets.

Key constructions

1. Antichain poset – For a poset (P=(P,\le)) let (2^{P}) denote its power set. Define a binary relation on subsets by
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