Uniformization and anti-uniformization properties of ladder systems

• Autorzy: Todd Eisworth , Gary Gruenhage , Oleg Pavlov , Paul Szeptycki
• Języki publikacji: EN

Abstrakty

EN

Natural weakenings of uniformizability of a ladder system on ω₁ 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 ω₁², 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 ♣, is considered.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E75: Applications of set theory
• 03E35: Consistency and independence results
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 3
• Strony: 189-213

Daty

wydano

2004

Twórcy

autor

Todd Eisworth

• Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A.

autor

Gary Gruenhage

• Department of Mathematics, Auburn University, 221 Parker Hall, Auburn, AL 36849, U.S.A.

autor

Oleg Pavlov

• Department of Mathematics, Towson University, 8000 York Road, Towson, MD 21252, U.S.A.

autor

Paul Szeptycki

• Atkinson Faculty, York University, Toronto, ON M3J 1P3, Canada

Identyfikatory

DOI

10.4064/fm181-3-1