On finite cohesiveness principle

2025/03/24 by Sun, Mengzhou
#03B30 #03C62 #03F35 #03H15 #05D10 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2503.18383

Abstract

We examine the cohesiveness principle applied to finite sequences of sets, referred to as fin-COH. We investigate its strength over different base theories: We show that over RCA^*₀, fin-COH implies IΣ₁⁰, which answers a question by Fiori-Carones, Kołodziejczyk and Kowalik. We also show that fin-COH is not provable over WKL₀.

Related

• Conservation theorems for the Cohesiveness Principle
• Cohesive avoidance and arithmetical sets
• Effective powers of ω over Δ₂ cohesive sets and infinite Π₁ sets without Δ₂ cohesive subsets
• Generalized cohesiveness
• Cofinitary groups and projective well-orders