In set theory, an extender is a set which represents an elementary embedding having large cardinal properties. A nonprincipal ultrafilter is the most basic case of an extender.
A (κ, λ)-extender can be defined as an elementary embedding of some model M of ZFC- (ZFC minus the power set axiom) having critical point κ ε M, and which maps κ to an ordinal at least equal to λ. It can also be defined as a collection of ultrafilters, one for each n-tuple drawn from λ.