6 citations · 9 across the 8 of their papers we have counts for
5 papers · 1 filter
Dependent finitely homogneneous rosy structures
Alf Onshuus, Pierre Simon
We study finitely homogeneous dependent rosy structures, adapting results of Cherlin, Harrington, and Lachlan proved for -stable -categorical structures. In particular, we pr…
A note on stability and NIP in one variable
Pierre Simon
A theory is NIP (resp. stable) if and only if every formula with parameters in two single variables is NIP (resp. does not have the order property).
Ordered graphs of bounded twin-width
Pierre Simon, Szymon Toruńczyk
We consider hereditary classes of graphs equipped with a total order. We provide multiple equivalent characterisations of those classes which have bounded twin-width. In particular…
Twin-width IV: ordered graphs and matrices
Édouard Bonnet, Ugo Giocanti, Patrice Ossona de Mendez +3
We establish a list of characterizations of bounded twin-width for hereditary, totally ordered binary structures. This has several consequences. First, it allows us to show that a…
Definable Equivariant Retractions in Non-Archimedean Geometry
Martin Hils, Ehud Hrushovski, Pierre Simon
For an algebraic group definable over a model of , or more generally a definable subgroup of an algebraic group, we study the stable completion $\widehat{G…