Recall that the Silver forcing $\mathbb{P}$ is defined as the set of all partial functions $p\in 2^{\le\omega}$ such that $\omega\setminus dom(p)$ is infinite. As usual, $p\le_\mathbb{P}q$ if $p$ extends $q$. The Silver model is the model $V$ obtained by the countable support iteration of length $\omega_2$ of the Silver forcing over a model of ZFC+CH.

I'm interested in values of the cardinal characteristics of the continuum in the van Douwen and Cichoń diagrams in $V$. Halbeisen in his brilliant book "Combintorial Set Theory" proves that:

$V\models \omega_1=\mathfrak{d}<\mathfrak{r}=\mathfrak{c}=\omega_2$.

It follows immediately that $V\models\mathfrak{u}=\mathfrak{i}=\omega_2$ and that all characteristics of the van Douwen diagram below $\mathfrak{d}$ are equal to $\omega_1$ in $V$. The only unknown in the diagram is the almost-disjointness number $\mathfrak{a}$.

**Question 1:** What is the value of $\mathfrak{a}$ in $V$?

Let $\mathcal{M}$ and $\mathcal{N}$ denote the ideal of meager subsets and the ideal of Lebesgue null subsets of $\mathbb{R}$, respectively. It can be shown that the ground model reals are non-meager in $V$, so $non(\mathcal{M})=\omega_1$ in $V$, and hence the left-hand half of the Cichoń diagram is also equal to $\omega_1$. Since $\mathfrak{d}=\omega_1$ in $V$, $cov(\mathcal{M})=\omega_1$ in $V$ as well. The rest of the Cichoń diagram is unfortunately unknown to me.

**Question 2:** What are the values of $cof(\mathcal{M})$, $non(\mathcal{N})$ and $cof(\mathcal{N})$ in $V$?

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