English

Hardy fields, the intermediate value property, and $\omega$-freeness

Logic 2019-04-03 v1 Classical Analysis and ODEs

Abstract

We discuss the conjecture that every maximal Hardy field has the Intermediate Value Property for differential polynomials, and its equivalence to the statement that all maximal Hardy field are elementarily equivalent to the differential field of transseries. As a modest but essential step towards establishing the conjecture we show that every maximal Hardy field is ω\omega-free.

Keywords

Cite

@article{arxiv.1904.01069,
  title  = {Hardy fields, the intermediate value property, and $\omega$-freeness},
  author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
  journal= {arXiv preprint arXiv:1904.01069},
  year   = {2019}
}

Comments

17 pp., to appear in S\'eminaire de structures alg\'ebriques ordonn\'ees

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