Related papers: Minimal pairs, minimal fields and implicit constan…

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…

We revisit the notion of initial sets by Xu and Cayrol, i.e., non-empty minimal admissible sets in abstract argumentation frameworks. Initial sets are a simple concept for analysing conflicts in an abstract argumentation framework and to…

We prove that if a strongly minimal non-locally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the underlying field.

In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an…

For unitary groups associated to a ramified quadratic extension of a $p$-adic field, we define various regular formal moduli spaces of $p$-divisible groups with parahoric levels, characterize exceptional special divisors on them, and…

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and…

In this paper, we study extensions of valuations over algebraic field extensions without the use of the Axiom of Choice. We show a bijection between the extensions of a valuation and the maximal ideals of the relative integral closure of…

We develop a framework of motivic integration in the style of Hrushovski--Kazhdan in arbitrary Hensel minimal fields of equicharacteristic zero. Hence our work generalizes that of Hrushovski--Kazhdan and Yin, but applies more broadly to…

This paper introduces new subdifferential concepts together with their main properties and place with respect to other subdifferential notions.

Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although…

We give a description of the minimal primes of the ideal generated by the 2 x 2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m x m minors of an m x n generic matrix when the…

We give an explicit characterization of all minimal value set polynomials in $\F_q[x]$ whose set of values is a subfield $\F_{q'}$ of $\F_{q}$. We show that the set of such polynomials, together with the constants of $\F_{q'}$, is an…

The main aim of this article is to study and develop valuation theory for Krasner hyperfields. In analogy with classical valuation theory for fields, we generalise the formalism of valuation rings to describe equivalence of valuations on…

The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from $2$ this theorem is extended here to function…

Non-archimedean fields with restricted analytic functions may not support a full exponential function, but they always have partial exponentials defined in convex subrings. On face of this, we study the first order theory of the class of…

Let $V$ be a valuation domain with quotient field $K$. Given a pseudo-convergent sequence $E$ in $K$, we study two constructions associating to $E$ a valuation domain of $K(X)$ lying over $V$, especially when $V$ has rank one. The first one…

We show that every definable nested family of closed and bounded subsets of a $P$-minimal field $K$ has non-empty intersection. As an application we answer a question of Darni\`ere and Halupczok showing that $P$-minimal fields satisfy the…

This paper proposes a new setup for studying pairs of structures. This new framework includes many of the previously studied classes of pairs, such as dense pairs of o-minimal structures, lovely pairs, fields with Mann groups, and…

I analyze $\mathcal{O}$-weakly immediate and $\mathcal{O}$-residual types in an o-minimal expansion of an ordered field $\mathbb{E}$, where $\mathcal{O}$ is a convex valuation ring. The main result is a characterization of those exponential…

We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral domain, then R is a field or a valuation ring or arises from…