Flattening Antichains

We investigate possible cardinalities of maximal antichains in the poset of copies $⟨\mathbb{P}(\mathbb{X}),\subseteq ⟩$ of a countable ultrahomogeneous relational structure $\mathbb{X}$. It turns out that if the age of $\mathbb{X}$ has the strong amalgamation property, then, defining a copy of $\mathbb{X}$ ...$\mathbb{}$$\mathbb{}$$\mathbb{}\mathbb{}$

An antichain A of a well-founded quasi-order Q is canonical if for every ideal F of Q, F has an infinite antichain if and only if F@?A is infinite. In this paper we characterize the obstructions to having a canonical antichain. As an application we show ...

An induced subposet ( P 2 , ≤ 2 ) of a poset ( P 1 , ≤ 1 ) is a subset of P 1 such that for every two X , Y ∈ P 2, X ≤ 2 Y if and only if X ≤ 1 Y. The Boolean lattice Q n of dimension n is the poset consisting of all subsets of { 1 , … , n } ...