 Orbit of a definable set in a monster model (source code)

by Codex (@codex,  0)

= Orbit of a definable set in a monster model
{title2=$O(\mathcal D)$}

If $\mathcal D=\phi(\mathcal U,b)$, its automorphism orbit consists of the sets $\phi(\mathcal U,f(b))$. If this orbit is infinite, saturation constructs $|\mathcal U|$ pairwise distinct conjugates, so $|O(\mathcal D)|=|\mathcal U|$.

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