REPRESENTATION FOR NONSTANDARD UNIVERSES

摘要

Nonstandard analysis is the branch of mathematical logic where, by using a conservatively extended framework, analysis is mainly done. A. Robinson devel-oped nonstandard analysis by using the ultraproduct that was the technique of mathematical logic [2]. So, many textbooks are written in an order in which non-standard analysis is done by first defining an ultrafilter, then making a model by the ultraproduct, and then using the model. In this article, no previous knowledge of mathematical logic is assumed. We begin with the definition of the desired nonstandard universe. Then we naturally find an ultrafilter and an ultrapower (see S2. Construction of a Nonstandard Universe). In the latter half, developing this construction, we obtain the title of represen-tation for nonstandard universes.