A large cardinal in the constructible universe
A Lindelöf space X such that is normal but not paracompact
A López-Escobar theorem for metric structures, and the topological Vaught conjecture
We show that a version of López-Escobar’s theorem holds in the setting of model theory for metric structures. More precisely, let denote the Urysohn sphere and let Mod(,) be the space of metric -structures supported on . Then for any Iso()-invariant Borel function f: Mod(,) → [0,1], there exists a sentence ϕ of such that for all M ∈ Mod(,) we have . This answers a question of Ivanov and Majcher-Iwanow. We prove several consequences, for example every orbit equivalence relation of a Polish group...
A matrix characterization of the maximal groups in
A method and tools for digital document and image reconstruction
A method for constructing some endomorphic universes
A minimal model for strong analysis
A modal logic of consistency
A Multiplication Of M-Relations
A multiplication of m-relations.
A new approach for studying fuzzy functional equations.
A new approach to construct uninorms via uninorms on bounded lattices
In this paper, on a bounded lattice , we give a new approach to construct uninorms via a given uninorm on the subinterval (or ) of under additional constraint conditions on and . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.
A new class of weakly countably determined Banach spaces
A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing ℓ¹(ℕ) is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If K is a compact space, then the space C(K) is SWCD if and only if K is countable.
A new class of weakly -analytic Banach spaces
In this paper we define and investigate a new subclass of those Banach spaces which are -analytic in their weak topology; we call them strongly weakly -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show that: (i) not...
A new construction of a Kurepa tree with no Aronszajn subtree
A new construction of non-constructible subset of ω
A new definition of the fuzzy set
The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
A new large cardinal and Laver sequences for extendibles
We define a new large cardinal axiom that fits between and in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.
A new proof of a theorem of Balcerzyk, Białynicki-Birula and Łoś
A new proof of James' sup theorem.
We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: "If a normed space E does not contain any asymptotically isometric copy of l1, then every bounded sequence of E' has a normalized l1-block sequence pointwise converging to 0".