A simple algebraic characterization of nonstandard extensions
Logic
2017-12-19 v1
Abstract
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.
Cite
@article{arxiv.1101.0548,
title = {A simple algebraic characterization of nonstandard extensions},
author = {Marco Forti},
journal= {arXiv preprint arXiv:1101.0548},
year = {2017}
}