TITLE: Is there an uncountable Borel almost disjoint family?
QUESTION [5 upvotes]: Here we are considering subsets $\mathcal{F}$ of $2^\omega$, which are in correspondence with families of subsets of $\omega$ (sets of "reals").  Such a family is Borel if it is a Borel subset of $2^\omega$ under the usual topology.
Such a family is almost disjoint if, for every pair $X\not=Y$ from $\mathcal{F}$, $X\cap Y$ is finite.
Note: the question originally only required that the symmetric difference between $X$ and $Y$ be infinite, which is substantially weaker.
Countable almost disjoint families can be constructed fairly trivially.  Uncountable almost disjoint families exist, and are a standard object of study in some branches of set theory.  However, the constructions I've seen do not result in a Borel set.  Can this be done?  Can $\mathcal{F}\subset 2^\omega$ be an uncountable Borel set which is an almost disjoint family?

REPLY [3 votes]: The answers to this question: Uncountable family of infinite subsets with pairwise finite intersections describe several Borel constructions of uncountable Borel families. (Usually: perfect families)