Epsilon-induction

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, -induction (epsilon-induction) is a variant of transfinite induction that can be used in set theory to prove that all sets satisfy a given property P[x]. If the truth of the property for x follows from its truth for all elements of x, for every set x, then the property is true of all sets. In symbols:

This principle, sometimes called the axiom of induction (in set theory), is equivalent to the axiom of regularity given the other ZF axioms. -induction is a special case of well-founded induction.

The name is most often pronounced "epsilon-induction", because the set membership symbol historically developed from the Greek letter .

See also[edit]