Keeping the covering number of the null ideal small

• Autorzy: Teruyuki Yorioka
• Języki publikacji: EN

Abstrakty

EN

It is proved that ideal-based forcings with the side condition method of Todorcevic (1984) add no random reals. By applying Judah-Repický's preservation theorem, it is consistent with the covering number of the null ideal being ℵ₁ that there are no S-spaces, every poset of uniform density ℵ₁ adds ℵ₁ Cohen reals, there are only five cofinal types of directed posets of size ℵ₁, and so on. This extends the previous work of Zapletal (2004).

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 231
• Numer: 2
• Strony: 139-159

Daty

wydano

2015

Twórcy

autor

Teruyuki Yorioka

• Department of Mathematics, Shizuoka University, Ohya 836, Shizuoka, 422-8529, Japan

Identyfikatory

DOI

10.4064/fm231-2-3