Extendibility of embeddings
Extending real-valued functions in βκ
An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.
Extensión de medidas difusas usando la esperanza monótona.
The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization...
Extension of Boolean homomorphisms with bounding semimorphisms.
Extension of functions with small oscillation
A classical theorem of Kuratowski says that every Baire one function on a subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer gradation of Baire one functions into small Baire classes. A Baire one function f is assigned into a class in this hierarchy depending on its oscillation index β(f). We prove a refinement of Kuratowski’s theorem: if Y is a subspace of a metric space X and f is a real-valued...
Extension of ZF-models to models with the scheme of choice
Extension principle and fuzzy-mathematical programming
Extensional subobjects in categories of -fuzzy sets
Two categories and of fuzzy sets over an -algebra are investigated. Full subcategories of these categories are introduced consisting of objects , , where is a subset of all extensional subobjects of an object . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.
Extensions of fuzzy connectives on ACDL
The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...
Extensions of the Graham-Leeb-Rothschild theorem.
Extensions with the approximation and cover properties have no new large cardinals
If an extension V ⊆ V̅ satisfies the δ approximation and cover properties for classes and V is a class in V̅, then every suitably closed embedding j: V̅ → N̅ in V̅ with critical point above δ restricts to an embedding j ↾ V amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above δ. This result extends work in [Ham01].
Extraction of fuzzy logic rules from data by means of artificial neural networks
The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...
Extraresolvability and cardinal arithmetic
Following Malykhin, we say that a space is extraresolvable if contains a family of dense subsets such that and the intersection of every two elements of is nowhere dense, where is a nonempty open subset of is the dispersion character of . We show that, for every cardinal , there is a compact extraresolvable space of size and dispersion character . In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) , 2) is extraresolvable and...
-ideals and -gaps in the Boolean algebras Ρ(ω)/I.
-section of Borel sets
Factorials of infinite cardinals
Factorization theorems for strong maps between matroids of arbitrary cardinality
In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.
Families of almost disjoint Hamel bases.
For infinite dimensional Banach spaces X we investigate the maximal size of a family of pairwise almost disjoint normalized Hamel bases of X, where two sets A and B are said to be almost disjoint if the cardinality of A ∩ B is smaller than the cardinality of either A or B.
Families of sets and functions
Fat P-sets in the Space ω*
We prove that-consistently-in the space ω* there are no P-sets with the ℂ-cc and any two fat P-sets with the ℂ⁺-cc are coabsolute.