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

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Ciesielski K., Millán A., Pawlikowski J.

Fundamenta Mathematicae

2003

tom 176

nr 2

143-155

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Ciesielski K.

1 Millán A.

1 Pawlikowski J.

1 2003

Wyniki wyszukiwania

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