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.
Alpha-theory: an elementary axiomatics for nonstandard analysis
BENCI, VIERI;DI NASSO, MAURO
2003-01-01
Abstract
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.File in questo prodotto:
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