Asymptotic Differential Algebra and Model Theory of Transseries
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
TL;DR
This paper develops the algebraic and model-theoretic foundations of transseries and related valued differential fields, providing new results on their structure and properties.
Contribution
It introduces a comprehensive algebraic framework for transseries and advances the understanding of their model theory with new positive results.
Findings
Decisive positive results on the model theory of transseries
Development of the algebra of differential fields of transseries
Insights into valued differential fields related to transseries
Abstract
We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra · Mathematical Dynamics and Fractals