On the Algebraic Complexity of Sets of Functions
On the algebraic structure of fuzzy sets of type 2
On the algebraic structure of the process of forming subsequences
On the averaging method for differential equations with delay.
On the axiom of choice for families of finite sets
On the axiomatisation of Boolean categories with and without medial.
On the Axiomatizability of Certain Classes of Modules.
On the Beth property in extension of Lukasiewicz logics.
On the Boffa alternative
Let G* denote a nonprincipal ultrapower of a group G. In 1986 M.~Boffa posed a question equivalent to the following one: if G does not satisfy a positive law, does G* contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.
On the Boolean structure generated by -points of
On the Borel class of the derived set operator
On the Borel class of the derived set operator. II
On the bounding, splitting, and distributivity numbers
The cardinal invariants of are known to satisfy that . We prove that all inequalities can be strict. We also introduce a new upper bound for and show that it can be less than . The key method is to utilize finite support matrix iterations of ccc posets following paper Ultrafilters with small generating sets by A. Blass and S. Shelah (1989).
On the bounds of the minimal length of sequences representing simply ordered sets.
On the Cantor-Bendixson rank of metabelian groups
We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank .
On the categorical semantics of elementary linear logic.
On the central limit theorem on IFS-events.
A probability theory on IFS-events has been constructed in [3], and axiomatically characterized in [4]. Here using a general system of axioms it is shown that any probability on IFS-events can be decomposed onto two probabilities on a Lukasiewicz tribe, hence some known results from [5], [6] can be used also for IFS-sets. As an application of the approach a variant of Central limit theorem is presented.
On the combinatorial principle P(c)
On the Compactness and Countable Compactness of in ZF
In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements " is countably compact" and " is compact"
On the complemented subspaces of the Schreier spaces
It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space generated by subsequences and , respectively, of the natural Schauder basis of are isomorphic if and only if and are equivalent. Further, admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of . It is also shown that there exists a complemented subspace spanned by a block basis of , which is not isomorphic to a subspace generated by a subsequence of , for every ....