Report
Effective infinitesimals in R
| العنوان: | Effective infinitesimals in R |
|---|---|
| المؤلفون: | Hrbacek, Karel, Katz, Mikhail G. |
| المصدر: | Real Analysis Exchange 48 (2023), no. 2, 365-380 |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Logic, Mathematics - Classical Analysis and ODEs, 26E35, 03A05, 03C25, 03C62, 03E70, 03H05 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.09672 |
| رقم الانضمام: | edsarx.2305.09672 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |