On two problems of quantum logics
On two tame algebras with super-decomposable pure-injective modules
Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...
On Tykhonov's theorem for convergence of solutions of slow and fast systems.
On types of fuzzy numbers under addition
We consider the question whether, for given fuzzy numbers, there are different pairs of -norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.
On Ulam's problem on families of measures
On unconditionally saturated Banach spaces
We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set 𝓐, in the Effros-Borel space of subspaces of C[0,1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y, with a Schauder basis, that contains isomorphic copies of every space X in the class 𝓐.
On universal null and universally measurable sets, II
On universal theories of metabelian groups and the Shmel'kin embedding.
On valued function fields III. Reductions of algebraic curves.
On variants of CM-triviality
We introduce a generalisation of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalises one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.
On Vitali sets and their unions
On weak Normality and Selectivity of Ultrafilters
On weaker forms of choice in second order arithmetic
On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces
We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of...
On Weakly Measurable Functions
We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
On weakly rigid monounary algebras
On what I do not understand (and have something to say): Part I
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history and side references...
On -statistically convergent double sequences of fuzzy numbers.
On -caliber and an application of Prikry’s partial order
We study the concept of -caliber as an alternative to the well known concept of caliber. -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, is a -caliber of . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.
On -extensions of .