• Borel Hierarchies in Infinite Products of Polish Spaces

• # Fulltext

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 $\mathcal{B}=\cup_{\xi &lt; \omega_1}\overline{\Sigma}_\xi$. We prove in the Lévy-Solovay model that

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

for $1\leq\xi &lt; \omega_1$.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019