# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Uniformization and anti-uniformization properties of ladder systems

### Tom 181 / 2004

Fundamenta Mathematicae 181 (2004), 189-213 MSC: Primary 03E05, 54D15; Secondary 03E35, 03E75. DOI: 10.4064/fm181-3-1

#### Streszczenie

Natural weakenings of uniformizability of a ladder system on $\omega _1$ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The existence of a thin, countably metacompact ladder system is used to construct interesting topological spaces: a countably paracompact and nonnormal subspace of $\omega _1^2$, and a countably paracompact, locally compact screenable space which is not paracompact. Whether the existence of a thin, countably metacompact ladder system is consistent is left open. Finally, the relation between the properties introduced and other well known properties of ladder systems, such as $\clubsuit$, is considered.

#### Autorzy

• Zoltán Balogh
• Todd EisworthDepartment of Mathematics
University of Northern Iowa
Cedar Falls, IA 50614, U.S.A.
e-mail
• Gary GruenhageDepartment of Mathematics
Auburn University
221 Parker Hall
Auburn, AL 36849, U.S.A.
e-mail
• Oleg PavlovDepartment of Mathematics
Towson University
Towson, MD 21252, U.S.A.
e-mail
• Paul SzeptyckiAtkinson Faculty
York University