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pro vyhledávání: '"Touchard, Pierre"'
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 tameness properties of the combinatorial structure to transfer to the al
Externí odkaz:
http://arxiv.org/abs/2403.20270
Generalised indiscernibles highlight a strong link between model theory and structural Ramsey theory. In this paper, we use generalised indiscernibles as tools to prove results in both these areas. More precisely, we first show that a reduct of an ul
Externí odkaz:
http://arxiv.org/abs/2311.05996
We investigate when an ordered abelian group $G$ is stably embedded in a given elementary extension $H$. We focus on a large class of ordered groups which includes maximal ordered groups with interpretable archimedean valuation. We give a complete an
Externí odkaz:
http://arxiv.org/abs/2308.09989
Autor:
Linzi, Alessandro, Touchard, Pierre
One can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field. First, we extend a result of Krasner by showing that t
Externí odkaz:
http://arxiv.org/abs/2211.05082
Autor:
Touchard, Pierre
In analogy to valued fields, we study model-theoretic properties of valued vector spaces with variable base field by proving transfer principles down to the skeleton and down to the value set and base field. For instance, we give a formula which comp
Externí odkaz:
http://arxiv.org/abs/2111.15516
Autor:
Touchard, Pierre1 (AUTHOR) pierre.touchard@kuleuven.be
Publikováno v:
Archive for Mathematical Logic. May2024, Vol. 63 Issue 3/4, p279-315. 37p.
Autor:
Touchard, Pierre
We show a transfer principle for the property that all types realised in a given elementary extension are definable. It can be written as follows: a Henselian valued fields is stably embedded in an elementary extension if and only if its value group
Externí odkaz:
http://arxiv.org/abs/2005.02363
Autor:
Touchard, Pierre
In the spirit of the Ax-Kochen-Ershov principle, we show that in certain cases the burden of a Henselian valued field can be computed in terms of the burden of its residue field and that of its value group. To do so, we first see that the burden of s
Externí odkaz:
http://arxiv.org/abs/1811.08756
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