Homogeneous universal $H$-fields
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- by Lou van den Dries and Philip Ehrlich PDF
- Proc. Amer. Math. Soc. 147 (2019), 2231-2234 Request permission
Abstract:
We consider derivations $\partial$ on Conway’s field $\mathbf {No}$ of surreal numbers such that the ordered differential field $(\mathbf {No},\partial )$ has constant field $\mathbb {R}$ and is a model of the model companion of the theory of $H$-fields with small derivation. We show that this determines $(\mathbf {No},\partial )$ uniquely up to isomorphism and that this structure is absolutely homogeneous universal for models of this theory with constant field $\mathbb {R}$.References
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Additional Information
- Lou van den Dries
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 59845
- Email: vddries@illinois.edu
- Philip Ehrlich
- Affiliation: Department of Philosophy, Ohio University, Athens, Ohio 45701
- MR Author ID: 233966
- Email: ehrlich@ohio.edu
- Received by editor(s): June 29, 2018
- Received by editor(s) in revised form: July 1, 2018
- Published electronically: February 6, 2019
- Communicated by: Heike Mildenberger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2231-2234
- MSC (2010): Primary 03C64; Secondary 12H05, 13N15, 26A12
- DOI: https://doi.org/10.1090/proc/14424
- MathSciNet review: 3937696