On The Range Of Boolean Transformation
On the Rank of Ext.
On the reducibility of the index sets of families of general recursive functions.
On the relation of three-valued logic to modal logic
On the relation of -reducibility between admissible sets.
On the relationship between weak compactness in L... and restricted second-order languages.
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