Related papers: More on the density zero ideal

The aim of this article is to study the ideal class monoid $\mathcal{C}\ell(S)$ of a numerical semigroup $S$ introduced by V. Barucci and F. Khouja. We prove new bounds on the cardinality of $\mathcal{C}\ell(S)$. We observe that…

It is well known to generalize the meagre ideal replacing aleph_0 by a (regular) cardinal lambda > aleph_0 and requiring the ideal to be lambda^+-complete. But can we generalize the null ideal? In terms of forcing, this means finding a…

In this article, we study combinatorial properties of a certain ideal on $\omega$, called the \emph{Splitting ideal}. We calculate its cardinal invariants and its position in the Kat\v{e}tov order among other definable ideals. We also study…

We prove the consistency of: for suitable strongly inaccessible cardinal lambda the dominating number, i.e., the cofinality of ^{lambda}lambda, is strictly bigger than cov_lambda(meagre), i.e. the minimal number of nowhere dense subsets of…

The main results of this paper are the construction, both rigourous and intuitive, of "the" intrinsic extension of the set of non negative integers N and the smallest over-field of R set which is continue (according to R.Dedekind). The aim…

The main goal of this note is to prove the following theorem. If $A_n$ is a sequence of measurable sets in a $\sigma$-finite measure space $(X, \mathcal{A}, \mu)$ that covers $\mu$-a.e. $x \in X$ infinitely many times, then there exists a…

Let $\mathcal{SN}$ be the $\sigma$-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\mathcal{SN}$ after finite support iterations. This is applied…

We unconditionally improve the uniformity in the Chebotarev density theorem for Galois extensions of number fields using nonabelian base change. This leads to the first theoretical improvement over Weiss's bound for the least norm of an…

We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal $\mathcal{SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which…

Assuming an integral quadratic polynomial with nonsingular quadratic part has a nontrivial zero on an integer lattice outside of a union of finite-index sublattices, we prove that there exists such a zero of bounded norm and provide an…

In this article we investigate the dual-shattering cardinal H, the dual-splitting cardinal S and the dual-reaping cardinal R, which are dualizations of the well-known cardinals h (the shattering cardinal, also known as the distributivity…

Using the concept of constant evasion to different sorts of suitable binary relations, we establish many cardinal invariants derived from the established cardinal invariants $\mathfrak{e}^\mathrm{const}_{n}$ and…

Let $N(\sigma,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $\sigma$ and imaginary part between $0$ and $T$. We provide explicit upper bounds for $N(\sigma,T)$ commonly referred to as a…

Generalizing Keisler's notion of regularity for ultrafilters, Taylor introduced degrees of regularity for ideals and showed that a countably complete nonregular ideal on $\omega_1$ must be somewhere $\omega_1$-dense. We prove a dichotomy…

New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…

We obtain a lower bound for the normalised height of a non-torsion subvariety $V$ of a C.M. abelian variety. This lower bound is optimal in terms of the geometric degree of $V$, up to a power of a ``log''. We thus extend the results of F.…

Let $X_N$ be a random trigonometric polynomial of degree $N$ with iid coefficients and let $Z_N(I)$ denote the (random) number of its zeros lying in the compact interval $I\subset\mathbb{R}$. Recently, a number of important advances were…

For non-binary codes the Elias bound is a good upper bound for the asymptotic information rate at low relative minimum distance, where as the Plotkin bound is better at high relative minimum distance. In this work, we obtain a hybrid of…

The work presents the first part of second edition of the previous edition of 2000 under the same title containing the proof (in ZF) of the nonexistence of inaccessible cardinals, now enriched and improved. This part contains the apparatus…

In the context of mod-Gaussian convergence, as defined previously in our work with J. Jacod, we obtain lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian with increasing covariance. This…