Related papers: Ideal weak QN-spaces

Let $\mathcal{Z(R)}$ be the set of zero divisor elements of a commutative ring $R$ with identity and $\mathcal{M}$ be the space of minimal prime ideals of $R$ with Zariski topology. An ideal $I$ of $R$ is called strongly dense ideal or…

This work is a part of my upcoming thesis [7]. We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$-degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2)…

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several…

In this paper it is proved that the ideal $I_w$ of the weak polynomial identities of the superalgebra $M_{1,1}(E)$ is generated by the proper polynomials $[x_1,x_2,x_3]$ and $[x_2,x_1][x_3,x_1][x_4,x_1]$. This is proved for any infinite…

In this paper we study a new ideal $\mathcal{WR}$. The main result is the following: an ideal is not weakly Ramsey if and only if it is above $\mathcal{WR}$ in the Kat\v{e}tov order. Weak Ramseyness was introduced by Laflamme in order to…

We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number $p>3$ and a squarefree number $N$ satisfying certain conditions, we study the Eisenstein part of the…

Let $\mathbb N$ be the set of positive integers, and denote by $\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the admissible ideals…

Given an ideal $I=(f_1,\ldots,f_r)$ in $\mathbb C[x_1,\ldots,x_n]$ generated by forms of degree $d$, and an integer $k>1$, how large can the ideal $I^k$ be, i.e., how small can the Hilbert function of $\mathbb C[x_1,\ldots,x_n]/I^k$ be? If…

We solve the last standing open problem from the seminal paper by J. Gerlits and Zs. Nagy, which was later reposed by A. Miller, T. Orenshtein and B. Tsaban. Namely, we show that under p = c there is a \delta-set that is not a \gamma-set.…

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal.…

Let $d_1,...,d_r$ be positive integers and let $I = (F_1,...,F_r)$ be an ideal generated by general forms of degrees $d_1,...,d_r$, respectively, in a polynomial ring $R$ with $n$ variables. When all the degrees are the same we give a…

This paper studies the combinatorics of ideals which recently appeared in ergodicity results for analytic equivalence relations. The ideals have the following topological representation. There is a separable metrizable space $X$, a…

This is a continuation of the paper [J. Symb. Log. 87 (2022), 1065--1092]. For an ideal $\mathcal{I}$ on $\omega$ we denote $\mathcal{D}_{\mathcal{I}}=\{f\in\omega^\omega: f^{-1}[\{n\}]\in\mathcal{I} \text{ for every $n\in \omega$}\}$ and…

An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_k)$ of real numbers is said to be lacunary $I$-convergent to a real number $\ell$,…

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a…

Hellsten \cite{MR2026390} gave a characterization of $\Pi^1_n$-indescribable subsets of a $\Pi^1_n$-indescribable cardinal in terms of a natural filter base: when $\kappa$ is a $\Pi^1_n$-indescribable cardinal, a set $S\subseteq\kappa$ is…

Let $W$ denote a linear space over a fixed field ${\mathbb F}$. We define the notions of weak $ISP$-system and weak $(u,v)$-system $\cal S=\{(U_i,V_i):~ 1\leq i\leq m\}$ of subspaces of $W$. We give upper bounds for the size of weak…

In this article, we extend the notion of multiplicity for weakly graded families of ideals which are bounded below linearly. In particular, we show that the limit $e_W(\mathfrak{I}):=\lim\limits_{n\to\infty}d!\frac{\ell_R(R/I_n)}{n^d}$…

We study the problem of whether $\mathcal{P}_w(^nE)$, the space of $n$-homogeneous polynomials which are weakly continuous on bounded sets, is an $M$-ideal in the space of continuous $n$-homogeneous polynomials $\mathcal{P}(^nE)$. We obtain…

We use reverse mathematics to analyze "iterated jump" versions of the following four principles: the atomic model theorem with subenumerable types (AST), the diagonally noncomputable principle (DNR), weak weak K\H{o}nig's lemma (WWKL), and…