On forcing projective generic absoluteness from strong cardinals

2018/07/06 by Trevor M. Wilson, Wilson, Trevor M. · 1 citation
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.1807.02206

openalex publication_date 2018/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

W.H. Woodin showed that if κ₁ < ⋯ < κ_n are strong cardinals then two-step \bfΣ¹_n+3 generic absoluteness holds after collapsing 2^2^κ_n to be countable. We show that this number can be reduced to 2^κ_n, and to κ_n⁺ in the case n = 1, but cannot be further reduced to κ_n.

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