Surreal numbers, derivations and transseries

DOI10.4171/JEMS/769zbMath1477.12006arXiv1503.00315WikidataQ59885496 ScholiaQ59885496MaRDI QIDQ1708554

Alessandro Berarducci, Vincenzo Mantova

Publication date: 23 March 2018

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.00315

zbMATH Keywords

transseriesdifferential fieldsHardy fieldssurreal numbers

Mathematics Subject Classification ID

Differential algebra (12H05) Ordinal and cardinal numbers (03E10) Model theory of ordered structures; o-minimality (03C64) Valued fields (12J10)

Related Items (11)

Book review of: M. Aschenbrenner et al., Asymptotic differential algebra and model theory of transseries ⋮ Exponential fields and Conway’s omega-map ⋮ ASYMPTOTIC ANALYSIS OF SKOLEM’S EXPONENTIAL FUNCTIONS ⋮ NUMBER SYSTEMS WITH SIMPLICITY HIERARCHIES: A GENERALIZATION OF CONWAY’S THEORY OF SURREAL NUMBERS II ⋮ Homogeneous universal $H$-fields ⋮ Surreal numbers with derivation, Hardy fields and transseries: a survey ⋮ The surreal numbers as a universal \(H\)-field ⋮ Transseries as germs of surreal functions ⋮ Generic derivations on o-minimal structures ⋮ Logarithmic hyperseries ⋮ SURREAL ORDERED EXPONENTIAL FIELDS

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