2 citations · 2 across the 2 of their papers we have counts for
6 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.…