The happy coexistence of mad families and Laver measurability

Asger Tornquist, David Schrittesser

Let $x$ denote a Laver real over $L$. We prove that in $L[x]$ there is a ${\Pi }_1^1$ infinite mad family. Since ${\Pi }_1^1$ and ${\Sigma }_2^1$ sets are Laver measurable in $L[x]$, this shows that…