The methods of nonstandard analysis are presented in elementary terms by postulating a few natural properties for an infinite "ideal" number alpha. The resulting axiomatic system, including a formalization of an interpretation of Cauchy's idea of infinitesimals, is related to the existence of ultrafilters with special properties, and is independent of ZFC. The Alpha-Theory supports the feeling that technical notions such as superstructure, ultrapower and the transfer principle are definitely not needed in order to carry out calculus with actual infinitesimals.
|Autori interni:||BENCI, VIERI|
DI NASSO, MAURO
|Autori:||BENCI V; DI NASSO M|
|Titolo:||Alpha-theory: an elementary axiomatics for nonstandard analysis|
|Anno del prodotto:||2003|
|Digital Object Identifier (DOI):||10.1016/S0723-0869(03)80038-5|
|Appare nelle tipologie:||1.1 Articolo in rivista|