Suppose we add the axiom to ZF that for any set $S$, and any partition $P$ of $S$, the cardinality of $P$ is less than or equal to the cardinality of $S$. It is known that the axiom of choice implies that axiom. My question is, is the converse true? Or are there models of ZF where that axiom holds but the axiom of choice doesn't?
2026-04-08 01:16:05.1775610965
Is this partition axiom equivalent to axiom of choice over ZF?
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