• Rana Barua

      Articles written in Proceedings – Mathematical Sciences

    • Borel Hierarchies in Infinite Products of Polish Spaces

      Rana Barua Ashok Maitra

      More Details Abstract Fulltext PDF

      Let 𝐻 be a product of countably infinite number of copies of an uncountable Polish space 𝑋. Let $\Sigma_\xi(\overline{\Sigma}_\xi)$ be the class of Borel sets of additive class 𝜉 for the product of copies of the discrete topology on 𝑋 (the Polish topology on 𝑋), and let $\mathcal{B}=\cup_{\xi < \omega_1}\overline{\Sigma}_\xi$. We prove in the Lévy-Solovay model that

      $$\overline{\Sigma}_\xi = \Sigma_\xi \cap\mathcal{B}$$

      for $1\leq\xi < \omega_1$.

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