TITLE: Almost disjoint functions of size $2^{\omega_1}$ in $\omega^{\omega_1}$
QUESTION [6 upvotes]: If we assume CH, it could be shown that there exists $2^{\omega_1}$ almost disjoint subsets of $\omega_1$. I'm wondering under CH if it's possible to show that there exists a family of almost disjoint functions from $\omega_1$ to $\omega$ of size $2^{\omega_1}$. Note 2 functions $f$ and $g$ are almost disjoint in $\omega_1$ if $|\{\alpha<\omega_1: f(\alpha)=g(\alpha)\}|<\omega_1$.

REPLY [2 votes]: It is consistent that there is no such family: If the non stationary ideal over $\omega_1$ is $\omega_2$-saturated, then there cannot be an almost disjoint family of functions from $\omega_1$ to $\omega$ of size $\omega_2$. Probably some forcing will give the other direction too.
From Jing Zhang's remark below, it follows that there is such a family in $L$.