Uncountable γ-sets under axiom $CPA_{cube}^{game}$

• Autorzy: Krzysztof Ciesielski , Andrés Millán , Janusz Pawlikowski
• Języki publikacji: EN

Abstrakty

EN

We formulate a Covering Property Axiom $CPA_{cube}^{game}$, which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in ℝ (which are strongly meager) as well as uncountable γ-sets in ℝ which are not strongly meager. These sets must be of cardinality ω₁ < 𝔠, since every γ-set is universally null, while $CPA_{cube}^{game}$ implies that every universally null has cardinality less than 𝔠 = ω₂. We also show that $CPA_{cube}^{game}$ implies the existence of a partition of ℝ into ω₁ null compact sets.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 26A03: Foundations: limits and generalizations, elementary topology of the line
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 2
• Strony: 143-155

Daty

wydano

2003

Twórcy

autor

Krzysztof Ciesielski

• Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, U.S.A.

autor

Andrés Millán

• Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, U.S.A.

autor

Janusz Pawlikowski

• Department of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/fm176-2-3