Related papers: Generalized Egorov's statement for ideals

We provide a counterexample to the Category Dichotomy in the framework of $\textsf{ZFC}$. That is, we prove the existence of an ideal on $\omega$ that is not Kat\v{e}tov below $\mathsf{nwd}$ and does not have restrictions above…

The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…

The generalized Effros-Hahn conjecture for groupoid C*-algebras says that, if G is amenable, then every primitive ideal of the groupoid C*-algebra C*(G) is induced from a stability group. We prove that the conjecture is valid for all second…

The dominated convergence theorem implies that if (f_n) is a sequence of functions on a probability space taking values in the interval [0,1], and (f_n) converges pointwise a.e., then the sequence of integrals converges to the integral of…

Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existence of a uniformizing function on a large set, relative to a…

A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some…

It is shown that for a subset $A\subset\R^n$ that has the global Gabrielov property, a Vitushkin-type estimate holds. Concrete examples are given for sub-level sets of certain classes of functions.

We prove a long-standing conjecture of Chudnovsky for very general and generic points in $\mathbb{P}_k^N$, where $k$ is an algebraically closed field of characteristic zero, and for any finite set of points lying on a quadric, without any…

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \N$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the…

Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic…

We show how to extend the theory of generalized Reynolds ideals, as introduced by B. K"ulshammer, from symmetric algebras to arbitrary finite-dimensional algebras (in positive characteristic). This provides new invariants of the derived…

In this article, we introduce a generalization of the concept of graded $r$-ideals in graded commutative rings with nonzero unity. Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity and $GI(R)$ be the set of all…

We show that the essentially algebraic theory of generalized algebraic theories, regarded as a category with finite limits, has a universal exponentiable arrow in the sense that any exponentiable arrow in any category with finite limits is…

In this note we present variants of Kostov's theorem on a versal deformation of a parabolic point of a complex analytic $1$-dimensional vector field. First we provide a self-contained proof of Kostov's theorem, together with a proof that…

A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic toric varieties over general fields. We also investigate a…

We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to model-companions and to amalgamation constructions \'a la Hrushovski-Fra\"iss\'e. Another notion of generic…

Local mean and individual (with respect to almost uniform convergence in Egorov's sense) ergodic theorems are established for actions of the semigroup $\mathbb R_+^d$ in symmetric spaces of measurable operators associated with a semifinite…

Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the…

In this note by using elementary considerations, we settle Fr\"oberg's conjecture for a large number of cases, when all generators of ideals have the same degree.