Surreal numbers with derivation, Hardy fields and transseries: a survey
From MaRDI portal
Publication:4635370
DOI10.1090/conm/697/14057zbMath1437.03132OpenAlexW4233903566WikidataQ59887178 ScholiaQ59887178MaRDI QIDQ4635370
Mickaël Matusinski, Vincenzo Mantova
Publication date: 16 April 2018
Published in: Ordered Algebraic Structures and Related Topics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/conm/697/14057
Model-theoretic algebra (03C60) Derivations and commutative rings (13N15) Model theory of ordered structures; o-minimality (03C64) Ordered fields (12J15)
Related Items (2)
Book review of: M. Aschenbrenner et al., Asymptotic differential algebra and model theory of transseries ⋮ Surreal Birthdays and Their Arithmetic
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hardy type derivations on fields of exponential logarithmic series
- Hardy type derivations on generalised series fields
- Hardy fields
- Hardy fields and existence of transexponential functions
- The elementary theory of restricted analytic fields with exponentiation
- \(H\)-fields and their Liouville extensions
- Ordered exponential fields
- Surreal numbers, derivations and transseries
- The surreal numbers as a universal \(H\)-field
- Asymptotic solutions of \(Y=F(x)Y\)
- The exponential-logarithmic equivalence classes of surreal numbers
- A tale of two Liouville closures
- Transseries and real differential algebra
- \(\kappa\)-bounded exponential-logarithmic power series fields
- Maximal fields with valuations
- Fields of surreal numbers and exponentiation
- Number systems with simplicity hierarchies: a generalization of Conway's theory of surreal numbers
- Asymptotic Differential Algebra and Model Theory of Transseries
- Notes on exponential-logarithmic terms
- Maps on Ultrametric Spaces, Hensel's Lemma, and Differential Equations Over Valued Fields
- Comparison of exponential-logarithmic and logarithmic-exponential series
- The Rank of a Hardy Field
- The limit behaviour of exponential terms
- Growth Properties of Functions in Hardy Fields
- On the Value Group of a Differential Valuation II
- Exponentiation in power series fields
- Logarithmic-Exponential Power Series
- Second Order Differential Equations over Hardy Fields
- On generalized series fields and exponential-logarithmic series fields with derivations
- The Absolute Arithmetic Continuum and the Unification Of all Numbers Great and Small
- Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
- Corrigendum to “Number Systems with Simplicity Hierarchies: A Generalization of Conway's Theory of Surreal Numbers”
- On Ordered Division Rings
- Logarithmic-exponential series
This page was built for publication: Surreal numbers with derivation, Hardy fields and transseries: a survey
