Definable Davies' Theorem

Abstract

We prove the following analogue of a Theorem of R.O. Davies: Every ${\Sigma }_2^1$ function $f:\mathbb{R}\times \mathbb{R}\to \mathbb{R}$ can be represented as a sum of rectangular ${\Sigma }_2^1$ functions if and only if all reals are constructible.

Final version, to appear in Fundamenta Mathematicae