Borel hierarchies in infinite products of Polish spaces

Details Borel hierarchies in infinite products of Polish spaces Borel hierarchies in infinite products of Polish spaces

2007-07-13

arxiv.org/abs/0707.1967v1

Mathematics

Logic

7 pages

Scientific paper

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 $1 \leq \xi < \omega_1$.

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