In model theory and set theory of some axiom system of set theory in the language of set theory is an end extension, if

1. is a substructure), and

2. .

.

are transitive sets.

A related concept is that of a top extension denotes the rank of a set.

Existence

Keisler and Morley showed that every countable model of ZF has an end extension which is also an elementary extension. on the Lévy hierarchy-elementary end extension.

References