Borel hierarchies in infinite products of Polish spaces
Abstract
Description
Let H be a product of countably infinite number of copies of an uncountable Polish space X. Let $Σ_ξ$ $(\bar Σ_ξ)$ be the class of Borel sets of additive class ξfor the product of copies of the discrete topology on X (the Polish topology on X), and let ${\cal B} = \cup_{ξ< ω_1} \barΣ_ξ$. We prove in the Lévy--Solovay model that \barΣ_ξ=Σ_ξ\cap {\cal B} for $1 \leq ξ< ω_1$.
7 pages
7 pages