A+ CATEGORY SCIENTIFIC UNIT

Analytic determinacy and $0^{\# }$ A forcing-free proof of Harrington’s theorem

Volume 160 / 1999

Ramez L. Sami Fundamenta Mathematicae 160 (1999), 153-159 DOI: 10.4064/fm-160-2-153-159

Abstract

We prove the following theorem: Given a⊆ω and $1 ≤ α < ω_1^{CK}$, if for some $η < ℵ_1$ and all u ∈ WO of length η, a is $Σ _α^0(u)$, then a is $Σ_α^0$. We use this result to give a new, forcing-free, proof of Leo Harrington's theorem: $Σ_1^1$-Turing-determinacy implies the existence of $0^#$.

Authors

  • Ramez L. Sami

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