On -subsets of naturals over abelian groups.
On σ-complete prime ideals in Boolean algebras
On σ-orthodistributivity
On -categorical theories of abelian groups
On -categorical theories of fields
On -saturated families
If there is no inner model with measurable cardinals, then for each cardinal there is an almost disjoint family of countable subsets of such that every subset of with order type contains an element of .
On ω-models which are not β-models
One of the Possible Formal Desribtions of Deducubility
One Parameter Subgroups and Nonstandard Analysis.
One-generated clones of operations on binary relations
Open and solved problems concerning polarized partition relations
We list some open problems concerning the polarized partition relation. We solve a couple of them, by showing that for every limit non-inaccessible ordinal α there exists a forcing notion ℙ such that the strong polarized relation holds in .
Open mappings on extremally disconnected compact spaces
Open problems posed at the eighth international conference on fuzzy set theory and applications
Several open problems posed during FSTA 2006 (Liptovský Ján, Slovakia) are presented. These problems concern the classification of strict triangular norms, Lipschitz t-norms, interval semigroups, copulas, semicopulas and quasi- copulas, fuzzy implications, means, fuzzy relations, MV-algebras and effect algebras.
Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)
Eighteen open problems posed during FSTA 2010 (Liptovský Ján, Slovakia) are presented. These problems concern copulas, triangular norms and related aggregation functions. Some open problems concerning effect algebras are also included.
Open topics in fuzzy coalitional games with transferable utility
Vagueness is one of the phenomena which cannot be separated from the real bargaining and cooperative situations. The aim of this paper is to offer a brief survey of the recent state-of-art of the modelling of vagueness in coalitional games with transferable utility. It may be recognized in two components of these games, namely, in vague structure of coalitions where each player may simultaneously participate in several of them, and in vague expectations of coalitional pay-offs. Both these cases...
Openly generated Boolean algebras and the Fodor-type reflection principle
We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is ℵ₂-projective. Previously it was known that this characterization of openly generated Boolean algebras follows from Axiom R. Since FRP is preserved by c.c.c. generic extension, we conclude in particular that this characterization is consistent with any set-theoretic assertion forcable by a c.c.c. poset starting from a model of FRP. A crucial step...
Opérateurs de mise en mémoire et types -positifs
Opérations de Hausdorff itérées et réunions croissantes de compacts
In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: iterations are needed in general to obtain the closure of a class under this operation. Increasing union is a particular Hausdorff operation, and we present the combinatorial tools which allow to study the power of various Hausdorff operations, and of their iterates. Besides countable increasing union, we study in detail a related Hausdorff operation,...
Operations, homomorphism and update versus relational database systems
Operators on C(ω^α) which do not preserve C(ω^α)
It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from onto itself such that if Y is a subspace of which is isomorphic to , then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from onto itself there is a subspace of which is isomorphic to on which the operator is an isomorphism.