Borel* Sets in the Generalised Baire Space

2012/09/18 by Tapani Hyttinen, Hyttinen, Tapani, Vadim Kulikov +1
Computer Science · Mathematics · #03-02 #03E47 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.LO #msc:03-02 #msc:03E47

paper · pdf · doi:10.48550/arxiv.1209.3933

19 pages

arxiv created 2012/09/18 · openalex publication_date 2012/09/18 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We start by giving a survey to the theory of Borel*(κ) sets in the generalized Baire space Baire(κ) = κ^κ. In particular we look at the relation of this complexity class to other complexity classes which we denote by Borel(κ), Δ¹₁(κ) and Σ¹₁(κ) and the connections between Borel*(κ)-sets and the infinitely deep language M_κ⁺κ. In the end of the paper we prove the consistency of Borel*(κ) ≠ Σ¹₁(κ).

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