On the representation of S5 algebras and their automorphism groups.
On the resemblance and recursive isomorphism types of partial recursive functions.
On the restricted equivalence for subclasses of propositional logic
On the selector of twin functions
A theorem is proved which could be considered as a bridge between the combinatorics which have a beginning in the dyadic spaces theory and the partition calculus.
On the semigroup of binary relations on a finite set
On the semigroup of fully indecomposable relations
On the sequence of models
On the set-theoretic strength of the n-compactness of generalized Cantor cubes
We investigate, in set theory without the Axiom of Choice , the set-theoretic strength of the statement Q(n): For every infinite set X, the Tychonoff product , where 2 = 0,1 has the discrete topology, is n-compact, where n = 2,3,4,5 (definitions are given in Section 1). We establish the following results: (1) For n = 3,4,5, Q(n) is, in (Zermelo-Fraenkel set theory minus ), equivalent to the Boolean Prime Ideal Theorem , whereas (2) Q(2) is strictly weaker than in set theory (Zermelo-Fraenkel set...
On the sharpness of the Stolz approach.
On the shift-window phenomenon of super-functions.
On the similarity of sets
On the simplicity and subdirect irreducibility of Boolean ultrapowers
On the solvability of systems of linear equations over the ring of integers
We investigate the question whether a system of homogeneous linear equations over is non-trivially solvable in provided that each subsystem with is non-trivially solvable in where is a fixed cardinal number such that . Among other results, we establish the following. (a) The answer is ‘No’ in the finite case (i.e., being finite). (b) The answer is ‘No’ in the denumerable case (i.e., and a natural number). (c) The answer in case that is uncountable and is ‘No relatively consistent...
On the splitting number and Mazurkiewicz's theorem
On the strength of several versions of Dirichlet's ("Pigeon-Hole"-) principle in the sense of first-order logic.
On the structure and classification of SOMAs: Generalizations of mutually orthogonal Latin squares.
On the structure of continuous uninorms
Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation in the unit interval with the neutral element . If operation is continuous, then or . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element , which is continuous in the open unit square may be given in ...
On the structure of intuitionistic algebras with relational probabilities.
Trillas ([1]) has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.
On the structure of numerical event spaces
The probability of the occurrence of an event pertaining to a physical system which is observed in different states determines a function from the set of states of the system to . The function is called a numerical event or multidimensional probability. When appropriately structured, sets of numerical events form so-called algebras of -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions with an inherent full set of states. A classical...
On the structure of perfect sets in various topologies associated with tree forcings
We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.