Adding highly undefinable sets over L

2023/11/04 by Mohammad Golshani, Saharon Shelah, Golshani, Mohammad +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Economic theories and models #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2311.02322

openalex publication_date 2023/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We sow that there exists a generic extension of the Gödel's constructible universe in which diamond holds and there exists a subset Y ⊆ ω₁ such that for stationary many δ< ω₁, the set Y ∩ δ is not definable in the structure (L_F(δ), ∈), where F(δ) > δ is the least ordinal such that L_F(δ)\models``δ is countable''.

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