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Preprint Number 1591

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1591. Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven
Hardy fields, the intermediate value property, and ω-freeness

Submission date: 1 April 2019


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-free.

Mathematics Subject Classification:

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Full text arXiv 1904.01069: pdf, ps.

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