# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## On the Class of Perfectly Null Sets and Its Transitive Version

### Tom 64 / 2016

Bulletin Polish Acad. Sci. Math. 64 (2016), 1-20 MSC: 03E05, 03E15, 03E35, 03E20. DOI: 10.4064/ba8029-5-2016 Opublikowany online: 17 June 2016

#### Streszczenie

We introduce two new classes of special subsets of the real line: the class of perfectly null sets and the class of sets which are perfectly null in the transitive sense. These classes may play the role of duals to the corresponding classes on the category side. We investigate their properties and, in particular, we prove that every strongly null set is perfectly null in the transitive sense, and that it is consistent with ZFC that there exists a universally null set which is not perfectly null in the transitive sense. Finally, we state some open questions concerning the above classes. Although the main problem of whether the classes of perfectly null sets and universally null sets are consistently different remains open, we prove some results related to this question.

#### Autorzy

• Michał KorchInstitute of Mathematics
University of Warsaw
02-097 Warszawa, Poland
e-mail
• Tomasz WeissInstitute of Mathematics
Cardinal Stefan Wyszyński University in Warsaw
01-938 Warszawa, Poland
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek