Related papers: On the structure of measurable filters on a counta…
In this study, we investigate quantum nonseparability between an observed system and a measuring apparatus, or multiple measuring apparatuses. We show that the physical meaning of the outcome of the measuring apparatus obtained by weak…
The Raisonnier Filter is a combinatorial object isolated by Jean Raisonnier in order to simplify Shelah's proof that if all $\boldsymbol{\Sigma}^1_3$ sets are Lebesgue-measurable then there is an inner model with an inaccessible cardinal.…
We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
A description of all subsemigroups of $M_2(\mathbb{C})$ which are given by a countable intersection of constructible sets is given. Furthermore, it is shown that they are intersections of constructible semigroups.
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli…
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
We exemplarily investigate how optical properties of single scatterers in interacting multi-particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core-shell…
In a typical two-slits experiments we face the question whether it is possible or not to attain knowledge about properties incompatible with Which-Slit property together with the measurement of the final impact point. A wide family of…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
An equivalence relation in the set of all square binary matrices is described in this work. It is discussed a combinatoric problem about finding the cardinal number and the elements of the factor set according to this relation. We examine…
We study an order relation on the fibers of a continuous map and its application to the study of the structure of compact spaces of uncountable weight.
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
We define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…
We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…
Using a new concept of conglomerated filter we demonstrate in a purely combinatorial way that none of Erd\"{o}s-Ulam filters or summable filters can be generated by a single statistical measure and consequently they cannot be represented as…