Extension of ZF-models to models with the scheme of choice
Extension pathology in regressive isols
Extension principle and fuzzy-mathematical programming
Extension theorems (vector measures on quantum logics)
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 Büchi's problem: Questions of decidability for addition and kth powers
We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...
Extensions of countable infinitary logic which preserve most of its nice properties.
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 -subsets to -subsets - existence versus constructability
Extensions of mappings of finite Boolean algebras to homomorphisms
Extensions of partially ordered partial abelian monoids
The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
Extensions of the Graham-Leeb-Rothschild theorem.
Extensions to Regressive Isols.
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...
e-степени гипериммунных ретрассируемых множеств.