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Toward a Model Theory for Transseries
Notre Dame Journal of Formal Logic 54 (3-4):279-310 (2013)
Abstract
The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.Author's Profile
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Citations of this work
Restricted analytic valued fields with partial exponentiation.Leonardo Ángel & Xavier Caicedo - 2025 - Archive for Mathematical Logic 64 (5):877-892.
Transseries and Todorov–Vernaeve’s asymptotic fields.Matthias Aschenbrenner & Isaac Goldbring - 2014 - Archive for Mathematical Logic 53 (1-2):65-87.
References found in this work
T-Convexity and Tame Extensions.Lou van den Dries & Adam H. Lewenberg - 1995 - Journal of Symbolic Logic 60 (1):74-102.
Topological differential fields.Nicolas Guzy & Françoise Point - 2010 - Annals of Pure and Applied Logic 161 (4):570-598.
A model complete theory of valued d-fields.Thomas Scanlon - 2000 - Journal of Symbolic Logic 65 (4):1758-1784.
Logarithmic-exponential series.Lou van den Dries, Angus Macintyre & David Marker - 2001 - Annals of Pure and Applied Logic 111 (1-2):61-113.
Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory.Saharon Shelah - 1971 - Annals of Mathematical Logic 3 (3):271-362.
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