# Category: Inner model theory

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.
L(R)
In set theory, L(R) (pronounced L of R) is the smallest transitive inner model of ZF containing all the ordinals and all the reals.
Code (set theory)
In set theory, a code for a hereditarily countable set is a set such that there is an isomorphism between (ω,E) and (X,) where X is the transitive closure of {x}. If X is finite (with cardinality n),
Chang's model
In mathematical set theory, Chang's model is the smallest inner model of set theory closed under countable sequences. It was introduced by Chang. More generally Chang introduced the smallest inner mod
Covering lemma
In the foundations of mathematics, a covering lemma is used to prove that the non-existence of certain large cardinals leads to the existence of a canonical inner model, called the core model, that is
Mouse (set theory)
In set theory, a mouse is a small model of (a fragment of) Zermelo–Fraenkel set theory with desirable properties. The exact definition depends on the context. In most cases, there is a technical defin