Berarducci, A and Mantova, V orcid.org/0000-0002-8454-7315 (2018) Surreal numbers, derivations and transseries. Journal of the European Mathematical Society, 20 (2). pp. 339-390. ISSN 1435-9855
Abstract
Several authors have conjectured that Conway’s field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, that is, the derivation is surjective.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, European Mathematical Society. This is an author produced version of a paper accepted for publication in Journal of the European Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Surreal numbers, transseries, Hardy fields, differential fields |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Mar 2017 12:05 |
Last Modified: | 01 Mar 2018 09:04 |
Status: | Published |
Publisher: | European Mathematical Society |
Identification Number: | 10.4171/JEMS/769 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109412 |