Borel hierarchies in infinite products of Polish spaces - Mathematics > Logic

Abstract: Let H be a product of countably infinite number of copies of an uncountablePolish space X. Let $\Sigma \xi$ $\bar {\Sigma} \xi$ be the class of Borelsets of additive class \xi for the product of copies of the discrete topologyon 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 $1 \leq \xi < \omega 1$.

Author: Rana Barua, Ashok Maitra

Source: https://arxiv.org/