We study Borel ideals $I$ on $\mathbb {N}$ with the Fréchet property such that the orthogonal $I^\perp $ is also Borel (where $A\in I^\perp $ iff $A\cap B$ is finite for all $B\in I$, and $I$ is Fréchet if $I=I^{\perp \perp }$). Let $\mathcal {B}$ be the