15 citations · 74 across the 12 of their papers we have counts for
5 papers · 1 filter
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…
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.…
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…
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…