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Recursion Theory by Liang Yu, Chi Tat Chong

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5.3.2 Sacks generic reals

A set Dimage is dense if for any condition T, there is an SD such that ST. A real x is Sacks generic if for any dense set Dimage arithmetical in image, there is a condition Timage such that x ∈ [T]. Note that by Lemma 5.3.2 and Lemma 5.3.4, for any sentence φ the set Dφ = {T | TφT ⊩¬φ} is dense and arithmetical in .

Lemma ...

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