The descriptive complexity of the set of Poisson generic numbers-Reference-Cited by-同舟云学术

The descriptive complexity of the set of Poisson generic numbers

Published:2024-05-09 Issue: Volume: Page:
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Becher Verónica¹^ORCID,Jackson Stephen²^ORCID,Kwietniak Dominik³^ORCID,Mance Bill⁴^ORCID

Affiliation:

1. Departamento de Computación, Facultad de Ciencias Exactas y Naturales & ICC, Universidad de Buenos Aires & CONICET, Argentina

2. Department of Mathematics, University of North Texas, General Academics Building 435, 1155 Union Circle, #311430, Denton, TX 76203-5017, USA

3. Faculty of Mathematics and Computer Science, Jagiellonian University in Kraków, ul. Łojasiewicza 6, 30-348 Kraków, Poland

4. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

Abstract

Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base [Formula: see text] is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base [Formula: see text] and not Poisson generic in base [Formula: see text] is complete for the class given by the differences between [Formula: see text] sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.

Funder

Agencia Nacional de Promoción Científica y Tecnológica de Argentina

NSF

The National Science Centre of Poland, NCN

National Science Centre, Poland, NCN

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061324500193