Peano and Osgood theorems via effective infinitesimals

Abstract

We provide effective proofs using infinitesimals of the global
versions of Peano's existence theorem and Osgood's theorem on maximal
solutions. We characterize all solutions in terms of infinitesimal perturbations.
Our proofs are more effective than traditional
non-infinitesimal proofs found in the literature. The background
logical structure is the internal set theory SPOT, conservative
over ZF.