About: End extension

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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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  • 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 . A related concept is that of a (also known as rank extension), where a model is a top extension of a model if and for all and , we have , where denotes the rank of a set. * v * t * e (en)
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  • 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 (en)
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  • End extension (en)
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