Related papers: On The Model Of Hyperrational Numbers With Selecti…
We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the…
Hyperproperties lift conventional trace-based languages from a set of execution traces to a set of sets of executions. From a formal-language perspective, these are sets of sets of words, namely hyperlanguages. Hyperautomata are based on…
A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its countable ultrapower over a cohesive set of natural numbers. A cohesive set is an…
We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several…
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
In this paper, we study a special type of ultrafilter which we call Shelah ultrafilter. We show that it is possible to add a Shelah ultrafilter using a special forcing notion. We also show that Shelah ultrafilters turn out to be…
We construct a random $n$-hypergraph for every $n$, in a given pseudofinite field.
A real number \alpha is called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to \alpha. The randomness of a recursively enumerable real \alpha can be characterized in various…
We present a novel conjecture concerning the additive representation of natural numbers using prime powers. Based on extensive computational verification, we conjecture that every integer n > 23 can be expressed as a sum of at most five…
We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit…
We answer two questions of Hindman, Stepr\=ans and Strauss, namely we prove that every strongly summable ultrafilter on an abelian group is sparse and has the trivial sums property. Moreover we show that in most cases the sparseness of the…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
The black-box nature of neural models has motivated a line of research that aims to generate natural language rationales to explain why a model made certain predictions. Such rationale generation models, to date, have been trained on…
Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. The 2-prime…
We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of…
The real type of a finite family of univariate polynomials characterizes the combined sign behavior of the polynomials over the real line. We derive an explicit formula for the number of real types subject to given degree bounds. For the…
We introduce and study rational symbolic powers of ideals in Noetherian rings. We give membership criteria for rational symbolic powers and discuss settings where they agree with integer symbolic powers. We investigate the binomial…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
We complete the characterization of the possible spectrum of regular ultrafilters D on a set I, where the spectrum is the set of infinite cardinals which are ultraproducts of finite cardinals modulo D.
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…