 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

A formula has <set-theoretic absoluteness> between these structures when both directions hold for every $\bar a\in M^n$:
$$
\boxed{(M,\in)\models\varphi(\bar a)\quad\Longleftrightarrow\quad(N,\in)\models\varphi(\bar a).}
$$
Equivalently, it is both a <downward absolute formula> and an <upward absolute formula> between them.

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