A simple algebraic characterization of nonstandard extensions

Details A simple algebraic characterization of nonstandard extensions A simple algebraic characterization of nonstandard extensions

2011-01-03

arxiv.org/abs/1101.0548v1

Mathematics

Logic

Scientific paper

We introduce the notion of "functional extension" of a set X, by means of two natural algebraic properties of the operator * on unary functions. We study the connections with ultrapowers of structures with universe X, and we give a simple characterization of those functional extensions that correspond to limit ultrapower extensions. In particular we obtain a purely algebraic proof of Keisler's characterization of nonstandard (= complete elementary) extensions.

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