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5 votes
1 answer
203 views

Uniformization of almost disjoint families

Suppose $\mathcal{F} \subseteq \mathcal{P} (\omega) $ is an almost disjoint family and $\aleph_0 < \vert \mathcal{F} \vert = \kappa < 2^{\aleph_0} $. Is it consistent that for some such cardinal ...
Matteo Casarosa's user avatar
9 votes
0 answers
388 views

On the role of $\diamondsuit$

The well-known axiom $\diamondsuit$ states that there is a sequence $\langle A_\alpha:\alpha<\omega_1\rangle$ (a $\diamondsuit$-sequence) of countable sets with the property that for any $A\...
Todd Eisworth's user avatar
11 votes
0 answers
490 views

$\Sigma^2_1$ and the Continuum Hypothesis

This is a follow up to Will Brian's answer to this recent question. In particular, quoting Brian: "In fact, Paul Larson has pointed out to me that the statement "$\phi$ and $\phi^{-1}$ are conjugate"...
Todd Eisworth's user avatar