arXiv Open Access 2023

Peano and Osgood theorems via effective infinitesimals

Karel Hrbacek Mikhail G. Katz

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Abstrak

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.

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Penulis (2)

Karel Hrbacek

Mikhail G. Katz

Format Sitasi

APA MLA BibTeX

Hrbacek, K., Katz, M.G. (2023). Peano and Osgood theorems via effective infinitesimals. https://arxiv.org/abs/2311.01374

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓