= Solution
A strict <partial order> is a <well-founded relation> when every nonempty subset $Y\subseteq P$ has a minimal member:
$$
\boxed{\exists y\in Y\ \forall x\in Y\ \neg(x<_P y).}
$$
In <ZFC> this is equivalent to the absence of an infinite descending sequence $p_0>_Pp_1>_P\cdots$. A descending sequence violates the minimal-member property; conversely, repeatedly choosing a predecessor from a subset with no minimal member constructs such a sequence using the <axiom of choice>.
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