-algebras of the monad -Fuzz
-equivalences generated by shape function on the real line
This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.
-extension as a method of construction of a generalized aggregation operator
Generalized aggregation operators are the tool for aggregation of fuzzy sets. The apparatus was introduced by Takači in [11]. -extension is a construction method of a generalized aggregation operator and we study it in the paper. We observe the behavior of a -extension with respect to different order relations and we investigate properties of the construction.
-Fuzzy topological concepts
-law of large numbers for fuzzy numbers
The notions of a -norm and of a fuzzy number are recalled. The law of large numbers for fuzzy numbers is defined. The fuzzy numbers, for which the law of large numbers holds, are investigated. The case when the law of large numbers is violated is studied.
Tableaux de Smullyan, ensembles de Hintikka et tout ça : un point de vue algébrique
On se propose de donner une interprétation algébrique (en calcul des propositions classiques) des notions d'arbres, d'ensembles de Hintikka, de la méthode des tableaux de Beth-Hintikka Smullyan.
Taclets: a new paradigm for constructing interactive theorem provers.
Frameworks for interactive theorem proving give the user explicit control over the construction of proofs based on meta languages that contain dedicated control structures for describing proof construction. Such languages are not easy to master and thus contribute to the already long list of skills required by prospective users of interactive theorem provers. Most users, however, only need a convenient formalism that allows to introduce new rules with minimal overhead. On the the other hand, rules...
Tame semiflows for piecewise linear vector fields
Let be a disjoint decomposition of and let be a vector field on , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to and prove that such semiflow belongs to the o-minimal structure . In particular, when is a continuous vector field and is an invariant subset of , our result implies that if is non-spiralling then the Poincaré first return map associated is also in .
Tarski Geometry Axioms – Part II
In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS (A5), betweenness...
Tarski's problem about the elementary theory of free groups has a positive solution.
Tavole semantiche per sistemi astratti di logica estensionale
Temi geometrici e di teoria della dimostrazione nelle logiche proposizionali di Łukasiewicz
Template iterations and maximal cofinitary groups
Jörg Brendle (2003) used Hechler’s forcing notion for adding a maximal almost disjoint family along an appropriate template forcing construction to show that (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that , the minimal size of a maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which enjoys certain combinatorial...
Tensor products of sequential effect algebras
Teorema de Ramsey aplicado a álgebras de Boole.
Some properties of Boolean algebras are characterized through the topological properties of a certain space of countable sequences of ordinals. For this, it is necessary to prove the Ramsey theorems for an arbitrary infinite cardinal. Also, we define continuous mappings on these spaces from vector measures on the algebra.
Teorie množin, její vznik a vývoj
Tests à la Hurewicz dans le plan
Nous donnons, pour une certaine catégorie de boréliens d'un produit de deux espaces polonais, comprenant les boréliens à coupes dénombrables, une caractérisation du type "test d'Hurewicz" de ceux ne pouvant pas être rendus différence transfinie d'ouverts par changement des deux topologies polonaises.
The algebra of first-order fuzzy logic
The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.
Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear metric space...
The algebraic uniqueness of the addition of natural numbers.