Alpha-theory: An elementary axiomatics for nonstandard analysis
作者： Vieri Benci , Mauro Di Nasso
DOI: 10.1016/S0723-0869(03)80038-5
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摘要: Abstract The methods of nonstandard analysis are presented in elementary terms by postulating a few natural properties for an infinite “ideal” number α. resulting axiomatic system, including formalization interpretation Cauchy's idea infinitesimals, is related to the existence ultrafilters with special properties, and independent ZFC. Alpha-Theory supports feeling that technical notions such as superstructure, ultrapower transfer principle definitely not needed order carry out calculus actual infinitesimals.
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