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Filling gaps in Hardy fields

Published:2024-08-23 Issue: Volume: Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Aschenbrenner Matthias¹^ORCID,van den Dries Lou²,van der Hoeven Joris³

Affiliation:

1. Kurt Gödel Research Center for Mathematical Logic , 27258 Universität Wien , 1090 Wien , Austria

2. Department of Mathematics , University of Illinois at Urbana-Champaign , Urbana , IL 61801 , USA

3. CNRS, LIX (UMR 7161) , École Polytechnique , Campus de l’École Polytechnique, 91120 Palaiseau , France

Abstract

Abstract We show how to fill “countable” gaps in Hardy fields. We use this to prove that any two maximal Hardy fields are back-and-forth equivalent.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0046/pdf

Reference31 articles.

1. N. L. Alling, A characterization of Abelian η α {\eta_{\alpha}} -groups in terms of their natural valuation, Proc. Natl. Acad. Sci. USA 47 (1961), 711–713.

2. N. L. Alling, On the existence of real-closed fields that are η α {\eta_{\alpha}} -sets of power ℵ α {\aleph_{\alpha}} , Trans. Amer. Math. Soc. 103 (1962), 341–352.

3. M. Aschenbrenner and L. van den Dries, Liouville closed H-fields, J. Pure Appl. Algebra 197 (2005), no. 1–3, 83–139.

4. M. Aschenbrenner, L. van den Dries and J. van der Hoeven, Asymptotic differential algebra and model theory of transseries, Ann. of Math. Stud. 195, Princeton University Press, Princeton 2017.

5. M. Aschenbrenner, L. van den Dries and J. van der Hoeven, On numbers, germs, and transseries, Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. II. Invited lectures, World Scientific, Hackensack (2018), 1–23.

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