4 papers
Coordinate recognition: General theory, Groups, and other surprises
I. Farah, K. Gannon, P. Touchard
A class of structures \emph{recognizes coordinates} if any reduced product of structures from said class witnesses a certain kind of rigidity phenomenon. We provide several equival…
Linear theories of global fields with absolute values
Arno Fehm, Pierre Touchard
We study the theory of a global field k as a k-vector space with a predicate for one of the absolute values on k. For example, we prove that in this language a global field with an…
Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Blaise Boissonneau, Aris Papadopoulos, Pierre Touchard
Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic ta…
Growing Spines Ad Infinitum
Blaise Boissonneau, Anna De Mase, Franziska Jahnke +1
We show that every non-trivial ordered abelian group is augmentable by infinite elements, i.e., we have for some non-trivial ordered abelian group …