Material set theory

Specification Axiom Schema

The Specification Axiom, technically an axiom schema, is a possible axiom schema of Material set theory: zf Let be a Predicative formula (i.e. unary definite condition) of set theory. Then,

which is to say, there exists a subset of containing all those elements of for which . By the Axiom of Extensionality such a set is unique, and we denote it using Set builder notation as

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