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Recursion Theory by Liang Yu, Chi Tat Chong

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Lemma 14.3.6. If x is image-random and yh x, then there is a recursive ordinal γ such that yT ximage(γ).

Proof. Since x is image-random, we have image = image. Let yh x. Then there is a formula with rank at most β0 < such that

By Lemma 13.1.1, there is a recursive ordinal ...

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