On \(\sigma\)-porous sets and Borel sets (Q583643)

The main result of the paper is the following: For any countable ordinal number \(\alpha\) there exists a Borel set \(C\subset R\) such that for each Borel set B of additive class \(\alpha\) the symmetric difference \(B\Delta\) C is not \(\sigma\)-porous. The proof is based on a ``well-parametrized'' uncountable family of pairwise disjoint non-\(\sigma\)-porous sets and the Lebesgue method of ``universal functions''. The Real Anal. Exch. is a good source for knowledge of \(\sigma\)-porous sets [especially in 13(1987- 88), 314-550 (1989; Zbl 0666.26003)].