Bohr compactifications of discrete structures
Volume 160 / 1999
Fundamenta Mathematicae 160 (1999), 101-151
DOI: 10.4064/fm_1999_160_2_1_101_151
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 $0^{#}$}.
