Year: 2023
Type: article
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.
Source: Journal of Logic and Analysis
Authors: Karel Hrbacek, Mikhail Katz
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4388327593