Strongly relativizing reals

Tyler Arant

For a real $f\in {\mathbb{N}}^{\mathbb{N}}$, it is in general not the case that every set which is both ${\Sigma }_1^1(f)$ and ${\Pi }_1^1(f)$ is the $f$-section of a ${\Delta }_1^1$ set. However, there ar…