Properties of ideals on generalized Cantor spaces
by
Jan Kraszewski
Mathematical Institute, University of Wroclaw, Poland

We shall discuss the properties of canonical ideals of

subsets of generalized Cantor spaces, for example the ideal of null

sets and of meagre sets.

In the 80's several people investigated relations between the ideal

of null subsets of the classical Cantor space and the ideal

of null subsets of the generalized Cantor space. One of the most important

questions was what were the connections between cardinal coefficients

(such as add, cov, non and cof) of them. The answer was given independently by

Cichon (unpublished) and Fremlin. Both authors obtained

almost the same results, except for two of them.

A natural question arose whether measure-theoretic tools were really

necessary to get these results. We give a complete answer to it.

In order to do this we extract the combinatorial principles that are

considered by both authors and show that similar results to those which

were obtained by them can be proved for a much wider class of ideals.

Date received: July 20, 2001