# ⓘ Extender, set theory. In set theory, an extender is a system of ultrafilters which represents an elementary embedding witnessing large cardinal properties. A no ..

## ⓘ Extender (set theory)

In set theory, an extender is a system of ultrafilters which represents an elementary embedding witnessing 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.

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