-Luzin sets, nonatomic -fields and -independent sets
Page 1 Next
Edward Grzegorek (2007)
Acta Universitatis Carolinae. Mathematica et Physica
René Guitart (1977)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Masahiro Inuiguchi (2014)
Kybernetika
To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the...
Stephen Watson, Zhou Hao-Xuan (1990)
Fundamenta Mathematicae
Márton Elekes, András Máthé (2009)
Fundamenta Mathematicae
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....
George Koumoullis (1984)
Fundamenta Mathematicae
Douglas Busch (1979)
Fundamenta Mathematicae
Christer Carlsson, Robert Fuller (1999)
Mathware and Soft Computing
We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r ≥ 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor r equals to zero. Generalizing our earlier results on fuzzy capital budegeting problems [Car99] we show that the possibility distribution of the {IRR} is a highly nonlinear function which is getting more and more unbalanced...
Jiří Karásek (1998)
Mathematica Bohemica
The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for -ary relational systems. -ary ordered sets are defined as special -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of or 3. The class of -ary ordered sets is then closed under the cardinal and ordinal operations.
Josef Šlapal (1993)
Czechoslovak Mathematical Journal
Taras O. Banakh (2004)
Commentationes Mathematicae Universitatis Carolinae
We calculate the cardinal characteristics of the -ideal of Haar null subsets of a Polish non-locally compact group with invariant metric and show that . If is the product of abelian locally compact groups , then , , and , where is the ideal of Lebesgue null subsets on the real line. Martin Axiom implies that and hence contains a Haar null subset that cannot be enlarged to a Borel or projective Haar null subset of . This gives a negative (consistent) answer to a question of...
Saharon Shelah, Zoran Spasojević (2002)
Publications de l'Institut Mathématique
Barbara Majcher-Iwanow (2000)
Commentationes Mathematicae Universitatis Carolinae
We study cardinal coefficients related to combinatorial properties of partitions of with respect to the order of almost containedness.
Andrzej Rosłanowski, Saharon Shelah (1998)
Fundamenta Mathematicae
We deal with some problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariants of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants.
Pelant, Jan (1975)
Seminar Uniform Spaces
István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy (2004)
Fundamenta Mathematicae
We show that if we add any number of Cohen reals to the ground model then, in the generic extension, a locally compact scattered space has at most levels of size ω. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of regular and of 0-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.
István Juhász, Lajos Soukup, William Weiss (2006)
Fundamenta Mathematicae
Let (α) denote the class of all cardinal sequences of length α associated with compact scattered spaces (or equivalently, superatomic Boolean algebras). Also put . We show that f ∈ (α) iff for some natural number n there are infinite cardinals and ordinals such that and where each . Under GCH we prove that if α < ω₂ then (i) ; (ii) if λ > cf(λ) = ω, ; (iii) if cf(λ) = ω₁, ; (iv) if cf(λ) > ω₁, . This yields a complete characterization of the classes (α) for all α < ω₂,...
Petr A. Biryukov (1980)
Commentationes Mathematicae Universitatis Carolinae
Stanisław Roguski (1990)
Colloquium Mathematicae
M.W. Bunder (1984)
Archiv für mathematische Logik und Grundlagenforschung
Page 1 Next