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## Z

Zermelo hierarchy See cumulative hierarchy.

Zermelo set theory Zermelo-Fraenkel set theory without the Axiom of Replacement. Abbreviated by the letter Z. See Zermelo-Fraenkel set theory.

Zermelo-Fraenkel set theory The formal theory whose axioms are: the Axiom of Extensionality, the Axiom of Regularity, the Axiom of Pairing, the Axiom of Separation, the Axiom of Union, the Axiom of Power Set, the Axiom of Infinity, the Axiom of Replacement, and the Axiom of Choice. This axiomatic theory is often abbreviated as ZFC (the letter C is for the Axiom of Choice).