On completely nonmeasurable unions

Assume that there is no quasi-measurable cardinal not greater than 2ω . We show that for a c.c.c. σ-ideal I with a Borel base of subsets of an uncountable Polish space, if A is a point-finite family of subsets from I then there is a subfamily of A whose union is completely nonmeasurable i.e. its intersection with every nonsmall Borel set does not belong to the σ-field generated by Borel sets and the ideal I. This result is a generalization of Four Poles Theorem (see [1]) and result from [3].

• Type: Journal
• Year: 2007
• Where: MLQ
• Authors: Szymon Zeberski
• Keywords: Borel Base, MLQ 2007, Quasi-measurable Cardinal, Uncountable Polish Space