On tightness in chain-net spaces
On Todorcevic orderings
The Todorcevic ordering 𝕋(X) consists of all finite families of convergent sequences in a given topological space X. Such an ordering was defined for the special case of the real line by S. Todorcevic (1991) as an example of a Borel ordering satisfying ccc that is not σ-finite cc and even need not have the Knaster property. We are interested in properties of 𝕋(X) where the space X is taken as a parameter. Conditions on X are given which ensure the countable chain condition and its stronger versions...
On tolerance analysis
On two Classical Results in the First Order Logic
On two complete sets in the analytical and the arithmetical hierarchies.
On two problems of mice
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...