Disjoint Borel Functions

2014/08/19 by Dan Hathaway, Hathaway, Dan
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1408.4200

openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For each a ∈ ℝ, we define a Borel function f_a : ℝ → ℝ which encodes a in a certain sense. We show that for each Borel g : ℝ → ℝ, f_a ∩ g = ∅ implies a ∈ Δ¹₁(c) where c is any code for g. We generalize this theorem for g in larger pointclasses Γ. Specifically, if Γ= \mathbfΔ¹₂, then a ∈ L[c]. Also for all n ∈ ω, if Γ= \mathbfΔ¹_{3 + n}, then a ∈ M_{1 + n}(c).

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