Alpha-theory: An elementary axiomatics for nonstandard analysis

DOI10.1016/S0723-0869(03)80038-5zbMath1038.26019MaRDI QIDQ1425690

Mauro Di Nasso, Vieri Benci

Publication date: 17 March 2004

Published in: Expositiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

nonstandard analysisalpha-calculusOmega-calculus

Mathematics Subject Classification ID

Nonstandard models in mathematics (03H05) Nonstandard analysis (26E35)

Related Items (24)

Ultrafunctions and Generalized Solutions ⋮ Ten misconceptions from the history of analysis and their debunking ⋮ Generalized solutions in PDEs and the Burgers' equation ⋮ A New Extension of the Riemann Integral ⋮ The Caccioppoli ultrafunctions ⋮ Nonstandard characterisations of tensor products and monads in the theory of ultrafilters ⋮ EUCLIDEAN NUMBERS AND NUMEROSITIES ⋮ Generalized functions beyond distributions ⋮ Non-Archimedean probability ⋮ A new approach to the \(Z\)-transform through infinite computation ⋮ Ultrafunctions and applications ⋮ A New Approach to Nonstandard Analysis ⋮ Fair infinite lotteries ⋮ Ultralarge lotteries: analyzing the lottery paradox using non-standard analysis ⋮ \(\mathcal {F}\)-finite embeddabilities of sets and ultrafilters ⋮ SET SIZE AND THE PART–WHOLE PRINCIPLE ⋮ Iterated hyper-extensions and an idempotent ultrafilter proof of Rado’s Theorem ⋮ Unnamed Item ⋮ Infinitesimals via Cauchy sequences: refining the classical equivalence ⋮ Generalized solutions of variational problems and applications ⋮ A Topological Approach to Non-Archimedean Mathematics ⋮ A simple algebraic characterization of nonstandard extensions ⋮ An improved setting for generalized functions: fine ultrafunctions ⋮ Numerosities of labelled sets: A new way of counting

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