Research Explorer

Project

Reverse Mathematics and Nonstandard Analysis: the actual infinite in the foundations of Mathematics
Code
3E018510
Duration
01 October 2010 → 31 January 2017
Funding
Regional and community funding: Special Research Fund, Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Analysis
    • History and foundations
Keywords
nonstandard analysis foundations of mathematics Reverse Mathematics the infinite
 
Project description
 

Reverse Mathematics (RM) unveils the striking phenomenon that theorems of ordinary Mathematics fall in only five equivalence classes, although there are infinitely many nonequivalent classes in Logic. My project analyzes RM where equality = is replaced with $\approx$, equality up to infinitesimals from Nonstandard Analysis. There are applications in Physics and the Philosophy of Science.