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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2001 | 167 | 3 | 277-289

## Another ⋄-like principle

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.

277-289

wydano
2001

### Twórcy

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