Material set theory

Axiom Schema of Replacement

The Axiom of Replacement, technically an axiom schema, is a possible axiom of Material set theory suggested by Abraham Fraenkel in the early 1920's¹: #m/def/set/zf Let 𝜑(𝑥,𝑦) be a Class function, i.e. a predicative formula such that (∀𝑥)(∃!𝑦)𝜑(𝑥,𝑦). Then,

which is to say, the image of a set under a mapping is a set.

#state/tidy | #lang/en | #SemBr