%0 Journal Article
%T Borel hierarchies in infinite products of Polish spaces
%A Rana Barua
%A Ashok Maitra
%J Mathematics
%D 2007
%I arXiv
%X Let H be a product of countably infinite number of copies of an uncountable Polish space X. Let $\Sigma_\xi$ $(\bar {\Sigma}_\xi)$ be the class of Borel sets of additive class \xi for the product of copies of the discrete topology on X (the Polish topology on X), and let ${\cal B} = \cup_{\xi < \omega_1} \bar{\Sigma}_\xi$. We prove in the L\'{e}vy--Solovay model that \bar{\Sigma}_\xi =\Sigma_{\xi}\cap {\cal B} for $1 \leq \xi < \omega_1$.
%U http://arxiv.org/abs/0707.1967v1