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Open topics in fuzzy coalitional games with transferable utility

Milan Mareš (2006)

Banach Center Publications

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

Sakaé Fuchino, Assaf Rinot (2011)

Fundamenta Mathematicae

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...

Opérations de Hausdorff itérées et réunions croissantes de compacts

Sylvain Kahane (1992)

Fundamenta Mathematicae

In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: ω 1 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,...

Operators on C(ω^α) which do not preserve C(ω^α)

Dale Alspach (1997)

Fundamenta Mathematicae

It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from C ( ω ω α ) onto itself such that if Y is a subspace of C ( ω ω α ) which is isomorphic to C ( ω ω α ) , 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 C ( ω ω α ) onto itself there is a subspace of C ( ω ω α ) which is isomorphic to C ( ω ω α ) on which the operator is an isomorphism.

Optimal matrices of partitions and an application to Souslin trees

Gido Scharfenberger-Fabian (2010)

Fundamenta Mathematicae

The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some useful properties, the n-optimal matrices of partitions. We use this to improve a decomposition result for strongly homogeneous Souslin trees. The latter is in turn applied to separate strong notions of rigidity of Souslin trees, thereby answering a considerable portion of a question of Fuchs and Hamkins.

Order with successors is not interprétable in RCF

S. Świerczkowski (1993)

Fundamenta Mathematicae

Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.

Ordered fields and the ultrafilter theorem

R. Berr, Françoise Delon, J. Schmid (1999)

Fundamenta Mathematicae

We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.

Ordered prime spectra of bounded D R l -monoids

Jiří Rachůnek (2000)

Mathematica Bohemica

Ordered prime spectra of Boolean products of bounded D R l -monoids are described by means of their decompositions to the prime spectra of the components.

Ordered Rings and Fields

Christoph Schwarzweller (2017)

Formalized Mathematics

We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].

Currently displaying 3341 – 3360 of 5989