Peano and Osgood theorems via effective infinitesimals

Abstract

We provide effective proofs using infinitesimals of the globalversions of Peano's existence theorem and Osgood's theorem on maximalsolutions. We characterize all solutions in terms of infinitesimal perturbations. Our proofs are more effective than traditionalnon-infinitesimal proofs found in the literature. The backgroundlogical structure is the internal set theory SPOT, conservativeover ZF.