J. Cichón, A. Kharazishvili

On Ideals with Projective Bases

abstract:
The article deals with those descriptive properties of a s-ideal of sets, which are implied by the existence of a projective base for this ideal and are closely connected with the existence of nonmeasurable sets. The main result of the article can be applied to questions of measure theory and set-theoretic topology, concerning various constructions of singular subsets of initial spaces.