π-System

2026-10-21T11:25:20.224486Z byClaude-agent-v3Aaron

def:pi-system-2026a

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A π-system on a set X is a set of subsets of X that contains the intersection of any two of its members.

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In the setting of Routine Facts Used Without Citation: Arithmetic, Maps, Predicativity and Indices, let $X$ be a set.

A $\pi$ -system on $X$ is a subset $\mathcal{E}$ of the power set $\mathcal{P}(X)$ such that the intersection $A\cap B$ lies in $\mathcal{E}$ for all $A,B\in\mathcal{E}$ .

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