Adding highly generic subsets of ω₂

2023/01/23 by Esfandiar Eslami, Eslami, Esfandiar, Golshani, Mohammad +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2301.09435

openalex publication_date 2023/01/23 · openalex created_date 2023/01/25 · openalex updated_date 2026/07/28

Abstract

Starting from the \rmGCH, we build a cardinal and \rmGCH preserving generic extension of the universe, in which there exists a set A ⊆ ω₂ of size ℵ₂ so that every countably infinite subset of A or ω₂ ∖ A is Cohen generic over the ground model.

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