15 citations · 74 across the 12 of their papers we have counts for
14 papers
About the algebraic closure of formal power series in several variables
Michel Hickel, Mickaël Matusinski
Let be a field of characteristic zero. We deal with the algebraic closure of the field of fractions of the ring of formal power series , . More pr…
Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy
Olivier Le Gal, Mickaël Matusinski, Fernando Sanz Sánchez
We introduce a notion of regular separation for solutions of systems of ODEs , where F is definable in a polynomially bounded o-minimal structure and . Gi…
Quantifier elimination for quasi-real closed fields
Mickaël Matusinski, Simon Müller
We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation. This unifies the same known results for algebraically closed valued fields a…
Exponential fields and Conway's omega-map
Alessandro Berarducci, Salma Kuhlmann, Vincenzo Mantova +1
Inspired by Conway's surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove…
About algebraic Puiseux series in several variables
Michel Hickel, Mickaël Matusinski
We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the r…
Surreal numbers with derivation, Hardy fields and transseries: a survey
Vincenzo Mantova, Mickaël Matusinski
The present article surveys surreal numbers with an informal approach, from their very first definition to their structure of universal real closed analytic and exponential field.…
On the algebraicity of Puiseux series
Michel Hickel, Mickaël Matusinski
We deal with the algebraicity of a Puiseux series in terms of the properties of its coefficients. We show that the algebraicity of a Puiseux series for given bounded degree is dete…
The valuation difference rank of a quasi-ordered difference field
Salma Kuhlmann, Mickael Matusinski, Francoise Point
There are several equivalent characterizations of the valuation rank of an ordered or valued field. In this paper, we extend the theory to the case of an ordered or valued {\it dif…
On generalized series fields and exponential-logarithmic series fields with derivations
Mickaël Matusinski
We survey some important properties of fields of generalized series and of exponential-logarithmic series, with particular emphasis on their possible differential structure, based…
A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields
Salma Kuhlmann, Mickael Matusinski, Ahuva C. Shkop
In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the…
The exponential-logarithmic equivalence classes of surreal numbers
Salma Kuhlmann, Mickaël Matusinski
In his monograph, H. Gonshor showed that Conway's real closed field of surreal numbers carries an exponential and logarithmic map. Subsequently, L. van den Dries and P. Ehrlich sho…
Hardy type derivations on fields of exponential logarithmic series
Salma Kuhlmann, Mickael Matusinski
We consider the valued field $\mathds{K}:=\mathbb{R}((Γ))$ of formal series (with real coefficients and monomials in a totally ordered multiplicative group ). We investigate ho…
Hardy type derivations on generalized series fields
Salma Kuhlmann, Mickael Matusinski
We consider the valued field $\mathds{K}:=\mathbb{R}((Γ))$ of generalized series (with real coefficients and monomials in a totally ordered multiplicative group ). We investigat…
Differential Puiseux theorem in generalized series fields of finite rank
Mickael Matusinski
We study differential equations where is a formal series in with coefficients in some field of \emph{generalized power series} $…