Reverse Mathematics and Nonstandard Analysis: the actual infinite in the foundations of Mathematics

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.