Related papers: Definability via the tilting correspondence
Let $(K,v)$ be a henselian valued field. Let $\mathbb{P}^{dless}\subset K[x]$ be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation $\,\approx\,$ on…
In this note, we show that the metaplectic theta correspondence is compatible with the tempered condition by directly estimating the matrix coefficients, without using the classification theorem.
We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a $Z$-group, is model-complete in the language of rings if the theory of its residue field is model-complete in…
We give a definition, in the ring language, of Z_p inside Q_p and of F_p[[t]] inside F_p((t)), which works uniformly for all $p$ and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula…
Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
There has been a long-standing question about whether being perfectoid for an algebra is local in the analytic topology. We provide affirmative answers for the algebras (e.g., over $\overline{\mathbb{Z}_p}$) whose spectra are inverse limits…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified. And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurable functions are also…
In this paper we show if R is a filtered ring then we can define a quasi valuation. And if R is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for R.
We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's…
In this note we study one-dimensional definable sets in power series fields with perfect residue fields. Using the description of automorphisms given by Schilling, in \cite{S44}, we show that such sets are unions of existentially definable…
In this paper, we characterize NIP henselian valued fields modulo the theory of their residue field, both in an algebraic and in a model-theoretic way. Assuming the conjecture that every infinite NIP field is either separably closed, real…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functoriality in tensor-triangular geometry from the viewpoint of…
We introduce the notion of n-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of n-APR tilting, and show that it preserves n-representation-finiteness. We give some combinatorial…
We prove in arbitrary characteristic that an immediate valued algebraic function field $F$ of transcendence degree 1 over a tame field $K$ is contained in the henselization of $K(x)$ for a suitably chosen $x\in F$. This eliminates…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…