O některých problémech souvisících s kardinální aritmetikou
O prvním Hilbertově problému (Hypotéza kontinua a axióm výběru)
O riešení niektorých nerozhodnutelných topologických problémov
OCA and towers in
We shall show that Open Coloring Axiom has different influence on the algebra than on . The tool used to accomplish this is forcing with a Suslin tree.
On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice
We study the deductive strength of properties under basic set-theoretical operations of the subclass E-Fin of the Dedekind finite sets in set theory without the Axiom of Choice ( AC ), which consists of all E-finite sets, where a set X is called E-finite if for no proper subset Y of X is there a surjection f:Y → X.
On a certain prewellordering
On a classification of denumerable order types and an application to the partition calculus
On a functional equation connected to the distributivity of fuzzy implications over triangular norms and conorms
Distributivity of fuzzy implications over different fuzzy logic connectives have a very important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems (see [9, 15] and [4]). Recently in some considerations connected with these distributivity laws, the following functional equation appeared (see [5]) where and is an unknown function. In this paper we consider in detail a generalized version of this equation, namely the equation where are functions...
On a Generalization of Permutable Equivalence Relations
On a local form of Lobachevski's functional equation
On a modification of axioms of general relations
Basic concepts concerning binary and ternary relations are extended to relations of arbitrary arities and then investigated.
On a modification of relational axioms
On a new class of distances between fuzzy numbers.
In the course of the studies on fuzzy regression analysis, we encountered the problem of introducing a distance between fuzzy numbers, which replaces the classical (x - y)2 on the real line. Our proposal is to compute such a function as a suitable weighted mean of the distances between the α-cuts of the fuzzy numbers. The main difficulty is concerned with the definition of the distance between intervals, since the current definitions present some disadvantages which are undesirable in our context....
On a paper by Karel Prikry concerning Ulam's problem on families of measures
On a perfect set
On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents
On a problem of Erdös and Tarski
On a problem of Nogura about the product of Fréchet-Urysohn -spaces
Assuming Martin’s Axiom, we provide an example of two Fréchet-Urysohn -spaces, whose product is a non-Fréchet-Urysohn -space. This gives a consistent negative answer to a question raised by T. Nogura.
On a Problem of Silver
On a problem of Steve Kalikow
The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.