Non-standard analysis revisited: An easy axiomatic presentation oriented towards numerical applications - Benci, Vieri; Cococcioni, Marco; Fiaschi, Lorenzo (Zielona Góra: Uniwersytet Zielonogórski)
Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson`s non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory.
Keywords: Alpha-Theory; non-standard analysis; non-Archimedean analysis; algorithmic numbers; non-Archimedean scientific computing