EFFECTIVE INFINITESIMALS IN R

Karel Hrbacek, Mikhail G. Katz

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)365-380
Number of pages16
JournalReal Analysis Exchange
Volume48
Issue number2
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 Michigan State University Press. All rights reserved.

Keywords

  • effective analysis
  • infinitesimals
  • nonstandard analysis

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