Related papers: Selective versions of $\theta$-density
We study connections between classical asymptotic density and c.e. sets. We prove that a c.e. Turing degree d is not low if and only if d contains a c.e. set A of density 1 which has no computable subsets of density 1, giving a natural…
We compare a traditional and non-traditional view on the subject of P-partitions, leading to formulas counting linear extensions of certain posets.
Let $\theta $ be a Salem number and $P(x)$ a polynomial with integer coefficients. It is well-known that the sequence $(\theta^n)$ modulo 1 is dense but not uniformly distributed. In this article we discuss the sequence $(P(\theta^n))$…
In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.
The main result of this paper is an improvement of the upper bound on the cardinal invariant ${\mathord{\mathrm{cov}}}^{\ast}({\mathcal{Z}}_{0})$ that was discovered by Raghavan and Shelah in an earlier paper. Here ${\mathcal{Z}}_{0}$ is…
We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
An infinite game on the set of real numbers appeared in Matthew Baker's work [Math. Mag. 80 (2007), no. 5, pp. 377--380] in which he asks whether it can help characterize countable subsets of the reals. This question is in a similar spirit…
We investigate the skewness of galaxy number density fluctuations as a possible probe to test gravity theories. We find that the specific linear combination of the skewness parameters corresponds to the coefficients of the second-order…
In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpositrionm (PPT) property can be readily checked. These densities were also investigated from a different…
This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…
In this article, we construct a $\theta$-density for the global sections of ample Hermitian line bundles on a projective arithmetic variety. We show that this density has similar behaviour to the usual density in the Arakelov geometric…
This paper provides a probabilist point of view about some results in analytic number theory. The main tool is the family of Zeta laws, which is a consolation for the non-existence of an uniform law on the set of integers. We prove the…
Under large cardinal hypotheses beyond the Kunen inconsistency -- hypotheses so strong as to contradict the Axiom of Choice -- we solve several variants of the generalized continuum problem and identify structural features of the levels…
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…
This dissertation highlights connections between the fields of neural networks, game theory and time series generation. The concept of antipredictability is explained, and the properties of time series that are antipredictable for several…
In Functional Analysis, certain conclusions apply to sequences, but they cannot be carried over when we consider nets. In fact, some nets, including sequences, can behave unexpectedly. In this paper we are interested in exploring the…
We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory…
The paper deals with real valued sequences and its distribution on real line.
We study two form of selective selective separability, $SS$ and $SS^+$, on countable spaces with an analytic topology. We show several Ramsey type properties which imply $SS$. For analytic spaces $X$, $SS^+$ is equivalent to have that the…