Alpha-theory: An elementary axiomatics for nonstandard analysis
By Vieri Benci, Mauro Di Nasso. 2003
62 citations recorded by the source corpus.
Abstract The methods of nonstandard analysis are presented in elementary terms by postulating a few natural properties for an infinite “ideal” number α. 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.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/d1c04fee1719ffb9c6cc2d03f54d400dabe863c0
How researchers see this paper
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In Computational Theory and Mathematics
- Marco Forti
- Mikhail G. Katz
- Vieri Benci
- David Sherry
- Piotr Błaszczyk
- Mauro Di Nasso
- Yaroslav D. Sergeyev
In Mathematical Physics
- David Sherry
- Mikhail G. Katz
- Piotr Błaszczyk
- Marco Forti
- Vieri Benci
- Mauro Di Nasso
- Yaroslav D. Sergeyev
In Theoretical Computer Science
Citations in the corpus
- The eightfold path to Nonstandard Analysis (2004, background): “Similarly, if two sequences are “eventually” different, then they take different values at infinity (see [5], Prop.”
- THE ULTRAPRODUCT CONSTRUCTION (2009, unknown): “Here is a condition which is a variant of a theorem of Benci and Di Nasso [2].”
- Ten Misconceptions from the History of Analysis and Their Debunking (2012, methodology): “Another axiomatic approach was proposed by Benci and Di Nasso [14].”