EFFECTIVE INFINITESIMALS IN R

Karel Hrbacek; Mikhail G. Katz

doi:https://doi.org/10.14321/realanalexch.48.2.1671048854

EFFECTIVE INFINITESIMALS IN R

Karel Hrbacek, Mikhail G. Katz

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We survey the effective foundations for analysis with infinitesimals developed by Hrbacek and Katz in 2021, and detail some applications. Theories SPOT and SCOT are conservative over respectively ZF and ZF+ADC. The range of applications of these theories illustrates the fact that analysis with infinitesimals requires no more choice than traditional analysis. The theory SCOT incorporates in particular all the axioms of Nelson’s Radically Elementary Probability Theory, which is therefore conservative over ZF+ADC.

Original language	English
Pages (from-to)	365-380
Number of pages	16
Journal	Real Analysis Exchange
Volume	48
Issue number	2
DOIs	https://doi.org/10.14321/realanalexch.48.2.1671048854
State	Published - 2023

Keywords

effective analysis
infinitesimals
nonstandard analysis

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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Cite this

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AB - We survey the effective foundations for analysis with infinitesimals developed by Hrbacek and Katz in 2021, and detail some applications. Theories SPOT and SCOT are conservative over respectively ZF and ZF+ADC. The range of applications of these theories illustrates the fact that analysis with infinitesimals requires no more choice than traditional analysis. The theory SCOT incorporates in particular all the axioms of Nelson’s Radically Elementary Probability Theory, which is therefore conservative over ZF+ADC.

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KW - nonstandard analysis

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EFFECTIVE INFINITESIMALS IN R

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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