We prove the following descriptive set-theoretic analogue of a theorem of R. O. Davies: Every Σ¹₂ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ¹₂ functions if and only if all reals are constructible.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-1-4,
author = {Asger T\"ornquist and William Weiss},
title = {Definable Davies' theorem},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {77-89},
zbl = {1189.03052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-1-4}
}
Asger Törnquist; William Weiss. Definable Davies' theorem. Fundamenta Mathematicae, Tome 205 (2009) pp. 77-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-1-4/