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.
-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.
Failure of completeness properties of intuitionistic predicate logic for constructive models
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
Fantastic filters of lattice implication algebras.
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.