In model theory and set theory, which are disciplines within mathematics, a model of some axiom system of set theory in the language of set theory is an end extension of , in symbols , if 1. * is a substructure of , (i.e., and ), and 2. * whenever and hold, i.e., no new elements are added by to the elements of . The second condition can be equivalently written as for all . For example, is an end extension of if and are transitive sets, and . * v * t * e
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