# 2000 seminar talk: Perfectly meager sets

Talk held by Tomek Bartoszynski (Boise State University, Rutgers University) at the KGRC seminar on 2000-06-09.

### Abstract

A set of reals X is perfectly meager if X is meager inside every perfect set P. Uncountable perfectly meager sets can be constructed in ZFC. In 1935 Marczewski asked if the product of perfectly meager sets is perfectly meager. In this talk I will discuss the answer to this question given by the following two theorems.

Theorem (Reclaw 1990) "No" is consistent with ZCF.

Theorem (T.B. 2000) "Yes" is consistent with ZCF.