Autor:	Hrbacek, Karel, Katz, Mikhail G.
Rok vydání:	2023
Předmět:	Mathematics - Logic Mathematics - Classical Analysis and ODEs 26E35 03A05 03C25 03C62 03E70 03H05
Zdroj:	Real Analysis Exchange 48 (2023), no. 2, 365-380
Druh dokumentu:	Working Paper
Popis:	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. Comment: 15 pages, to appear in Real Analysis Exchange
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.09672 Zobrazit plný text záznamu View this record from Arxiv