We study the problem of existence of maximal chains in the Turing degrees. We show that:
1. ZF + DC + “There exists no maximal chain in the Turing degrees” is equiconsistent with ZFC + “There exists an inaccessible cardinal”
2. For all a ∈ 2ω, (ω1)L[a] = ω1 if and only if there exists a [a] maximal chain in the Turing degrees. As a corollary, ZFC + “There exists an inaccessible cardinal” is equiconsistent with ZFC + “There is no (bold face) maximal chain of Turing degrees”.
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