Peano and Osgood theorems via effective infinitesimals

Karel Hrbacek; Mikhail G. Katz

doi:10.4115/jla.2023.15.6

Peano and Osgood theorems via effective infinitesimals

Karel Hrbacek
, Mikhail G. Katz

Department of Mathematics

City University of New York

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We provide choiceless 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.

Original language	English
Article number	6
Journal	Journal of Logic and Analysis
Volume	15
DOIs	https://doi.org/10.4115/jla.2023.15.6
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Journal of Logic and Analysis. All rights reserved.

Keywords

Osgood theorem
Peano existence theorem
axiom of choice
effective proofs
nonstandard analysis

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10.4115/jla.2023.15.6

Cite this

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KW - Peano existence theorem

KW - axiom of choice

KW - effective proofs

KW - nonstandard analysis

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Peano and Osgood theorems via effective infinitesimals

Abstract

Bibliographical note

Keywords

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