Hereditarily finite set

Set

definiendum	$V_\omega$ in it
postulate	$\emptyset\in V_\omega$
for all	$x\in V_\omega$
postulate	${\mathcal P}(x)\in V_\omega$
postulate	$x = \emptyset\ \lor\ \exists (y\in V_\omega).\ x = {\mathcal P}(y)$

Discussion

Idea

This is the set of all finite sets constructable when starting with $\emptyset$ . It's the smallest infinite Grothendieck universe, as well as a model of ZFC.

Hereditarily finite set

Set

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Hereditarily finite set

Set

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