Another ⋄-like principle

• Autorzy: Michael Hrušák
• Języki publikacji: EN

Abstrakty

EN

A new ⋄-like principle $⋄_{𝔡}$ consistent with the negation of the Continuum Hypothesis is introduced and studied. It is shown that $¬ ⋄_{𝔡}$ is consistent with CH and that in many models of 𝔡 = ω₁ the principle $⋄_{𝔡}$ holds. As $⋄_{𝔡}$ implies that there is a MAD family of size ℵ₁ this provides a partial answer to a question of J. Roitman who asked whether 𝔡 = ω₁ implies 𝔞 = ω₁. It is proved that $⋄_{𝔡}$ holds in any model obtained by adding a single Laver real, answering a question of J. Brendle who asked whether 𝔞 = ω₁ in such models.

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: 2001
• Tom: 167
• Numer: 3
• Strony: 277-289

Daty

wydano

2001

Twórcy

autor

Michael Hrušák

• Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3

Identyfikatory

DOI

10.4064/fm167-3-5