Related papers: Construction du hens\'elis\'e d'un corps valu\'e
We show that exchangeable structures such as Polya urn model and Chinese restaurant process can be constructed from sets with a real number of elements. From this construction, the exchangeability of these structures becomes obvious and the…
A description is an entity that can be interpreted as true or false of an object, and using feature structures as descriptions accrues several computational benefits. In this paper, I create an explicit interpretation of a typed feature…
We consider the ordered field which is the completion of the Puiseux series field over \bR equipped with a ring of analytic functions on [-1,1]^n which contains the standard subanalytic functions as well as functions given by t-adically…
In this paper we prove a duality for constructible sheaves on conically smooth stratified spaces. Here we consider sheaves with values in a stable and bicomplete $\infty$-category equipped with a closed symmetric monoidal structure, and in…
We give a characterization of finitely ramified $\omega$-pseudo complete valued fields of mixed characteristic $(0, p)$, with fixed residue field $k$ and value group $G$ of cardinality $\aleph_{1}$, in terms of a Hahn-like construction over…
In this note we construct a canonical lifting of arbitrary Poisson structures on a manifold to its algbera of densities. Using this construction we proceed to classify all extensions of a fixed structure on the original manifold to its…
In this paper we study domination in an Ax-Kochen/Ershov style results for henselian valued fields of equicharacteristic zero for elements in the home sort.
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…
Working in Zermelo-Fraenkel Set Theory with Atoms over an $\omega$-categorical $\omega$-stable structure, we show how \emph{infinite} constructions over definable sets can be encoded as \emph{finite} constructions over the Stone-\v{C}ech…
We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central…
We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.
In the article "Construction of the discrete hull for the combinatorics of a regular pentagonal tiling of the plane" we gave the construction of a discrete hull for a combinatorial pentagonal tiling of the plane. In this paper, we give the…
We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field,…
Henselian elements are roots of polynomials which satisfy the conditions of Hensel's Lemma. In this paper we prove that for a finite field extension $(F|L,v)$, if $F$ is contained in the absolute inertia field of $L$, then the valuation…
This article provides formal definitions characterizing well-formed composition of components in order to guarantee their safe deployment and execution. Our work focuses on the structural aspects of component composition; it puts together…
We present methods of constructing examples of quandles of order 3n, where n is greater or equal to 3. The necessary and sufficient conditions for the constructed examples to be (i) connected (ii) group (conjugate) (iii) involutory and (iv)…
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of…
We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived infinity-category…
In this paper, we first present a new secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, we apply the construction using as initial functions some specific bent functions and…