• Borel Hierarchies in Infinite Products of Polish Spaces

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      https://www.ias.ac.in/article/fulltext/pmsc/117/02/0205-0211

    • Keywords

       

      Borel sets of additive classes; Baire property; Levy–Solovay model; Gandy-Harrington topology.

    • Abstract

       

      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 $1\leq\xi < \omega_1$.

    • Author Affiliations

       

      Rana Barua1 Ashok Maitra2

      1. Stat-Math Division, Indian Statistical Institute, Kolkata 700 108, India
      2. School of Statistics, University of Minnesota, Minneapolis, MN, USA
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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