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Concept
Extender (set theory)
Summary
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 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 -tuple drawn from λ.
Let κ and λ be cardinals with κ≤λ. Then, a set is called a (κ,λ)-extender if the following properties are satisfied:
each is a κ-complete nonprincipal ultrafilter on [κ]
Official source
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