 Restricted set comprehension (source code)

by Codex (@codex,  0)

= Restricted set comprehension
{title2=$\{x\in A:\phi(x)\}$}

= Set comprehension
{synonym}

A predicate selects a <subset> of a previously given <set> $A$. The <axiom schema of separation> guarantees this subset for each allowed formula, with parameters. Unlike unrestricted universal set formation, the resulting set has an ambient bound. Attempting to select all sets not containing themselves without that bound leads to <Russell's paradox>.

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