相关论文: Minimal pairs, minimal fields and implicit constan…
We study the existence of pairwise stable allocations in matching markets with contracts and propose a domain restriction that guarantees their existence. Specifically, we define pseudo-substitutable preferences, a domain that strictly…
We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical…
The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of…
We study infinite groups interpretable in three families of valued fields: $V$-minimal, power bounded $T$-convex, and $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and that if $G$ is dp-minimal then it…
We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…
We derive basic properties of minimal extensions of local rings and their restrictions to subrings. Some applications are included to subrings of truncated polynomial rings.
We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain…
The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to…
We improve results of Belair, Macintyre, and Scanlon on valued fields with a valuation preserving automorphism by weakening their assumptions on the residue difference field. In the equicharacteristic zero case we also determine the induced…
Let $(K,v)$ be a valued field. We review some results of MacLane and Vaqui\'e on extensions of $v$ to valuations on the polynomial ring $K[x]$. We introduce certain MacLane-Vaqui\'e chains of residually transcendental valuations, and we…
Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring and a $T$-derivation. If this derivation is continuous with respect…
We develop a first-order theory of ordered transexponential fields in the language $\{+,\cdot,0,1,<,e,T\}$, where $e$ and $T$ stand for unary function symbols. While the archimedean models of this theory are readily described, the study of…
In the talk \cite{vandendries-matthias-} presented at Logic and Foundations section of ICM-2018, Rio de Janeiro, the authors analyze, under a model-theoretic perspective, three ways to enrich the real continuum by infinitesimal and infinite…
We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions…
A first order expansion of $(\mathbb{R},+,<)$ is dp-minimal if and only if it is o-minimal. We prove analogous results for algebraic closures of finite fields, $p$-adic fields, ordered abelian groups with only finitely many convex subgroups…
We show that a pure transcendental, immediate extension of valuation rings $V\subset V'$ containing a field is a filtered union of smooth $V$-subalgebras of $V'$.
In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…
Auxiliary string fields are introduced in light-cone gauge string field theory in order to express contact interactions as contractions of cubic vertices. The auxiliary field in the purely closed-string bosonic theory may be given a…
In this short letter we present a class of remarkably simple solutions to Witten's open string field theory that describe marginal deformations of the underlying boundary conformal field theory. The solutions we consider correspond to…
The paper proves the intermediate value theorem for polynomials and power series over a valued field with divisible valuation group and infinite residue field. Some further results on the behaviour of the valuation are obtained using…