I know that ZF is not finitely axiomatizable, but what about Z (i.e. ZF without Replacement)?
2026-04-13 07:03:22.1776063802
Is Zermelo set theory finitely axiomatizable?
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No. It is not.
You can find the proof as Theorem 8 in:
(The article also appears on Mathias' homepage without the need for a paywall)