Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Cayley theorem for posets

Ivan Chajda, Helmut Länger

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.

A Cayley theorem for 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.
Paper Structure (2 theorems, 5 equations)

This paper contains 2 theorems, 5 equations.

Key Result

Lemma 1

$(A(\mathbf P),\le)$ is a poset.

Theorems & Definitions (7)

  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Example 3
  • Remark 4
  • Example 5