Alpha-theory: An elementary axiomatics for nonstandard analysis
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Publication:1425690
DOI10.1016/S0723-0869(03)80038-5zbMath1038.26019MaRDI QIDQ1425690
Publication date: 17 March 2004
Published in: Expositiones Mathematicae (Search for Journal in Brave)
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
Cites Work
- Foundations of infinitesimal stochastic analysis
- Homogeneity problems in the theory of Cech compactifications
- Eine Erweiterung der Infinitesimalrechnung
- Set theory. An introduction to independence proofs
- Proper forcing
- Model theory.
- Cauchy and the infinitely small
- Non-nonstandard analysis: Real infinitesimals
- Loeb measures in practice: Recent advances. EMS lectures 1997
- Numerosities of labelled sets: A new way of counting
- A ring homomorphism is enough to get nonstandard analysis
- The use of double nonstandard enlargements in topology
- Calculus is Algebra
- On Cauchy's Notion of Infinitesimal
- THE CONCEPT OF ‘VARIABLE’ IN NINETEENTH CENTURY ANALYSIS
- Internal set theory: A new approach to nonstandard analysis
- Ultrafilters which extend measures
- Developments in Constructive Nonstandard Analysis
- Applications of Nonstandard Analysis in Additive Number Theory
- An axiomatic presentation of the nonstandard methods in mathematics
- Ultrafilters on a countable set
- Cauchy, Convergence and Continuity
- Comparison of the axioms of local and universal choice
- The Rudin-Keisler Ordering of P-Points
- Non-standard analysis
- Reuniting the antipodes---constructive and nonstandard views of the continuum. Symposium proceedings, San Servolo, Venice, Italy, May 16--22, 1999
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