# $\mathfrak{p}=\mathfrak{b}=\mathfrak{a}=\aleph_1$ and $\mathfrak{d}=\mathfrak{c}=\kappa$

Asumme tha in $M$, $CH$ holds and $\kappa>\aleph_0$ and $\kappa^{\aleph_0}=\kappa$. Let $K$ be $Fn(\kappa,2)$-generic over $M$.

Question:

Then we can say in $M[K]$ that:

$(i)$ $\mathfrak{p}=\mathfrak{b}=\mathfrak{a}=\aleph_1$ and $\mathfrak{d}=\mathfrak{c}=\kappa$ ?

Where

$\mathfrak{c}=2^{\aleph_0}$ the size of the continuum.

$\mathfrak{d}$, is the least size of a $\mathfrak{d}$ominating family.

$\mathfrak{b}$, is the least size of an un$\mathfrak{b}$ounded family.

$\mathfrak{p}$, is the least size of family $\mathcal{E}\subseteq [\omega]^\omega$ such that $\mathcal{E}$ has the SFIP and there does not exist any $\mathfrak{p}$seuod-intersection of $\mathcal{E}$.

$\mathfrak{a}$, is the least size of an infinite m$\mathfrak{a}$d family.

• Why the vote to close? – Noah Schweber Mar 14 '15 at 1:42