= Extender (set theory)
{wiki=Extender_(set_theory)}
In set theory, particularly in the context of large cardinals, an **extender** is a type of structure used to define certain kinds of elementary embeddings. Extenders play a crucial role in the study of large cardinal properties and help in constructing models of set theory, especially in the context of the **inner model theory**. An extender is a specific kind of object that can be used to generate ultrapowers. It is characterized by its ability to extend a certain level of consistency within set theory.
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