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|Title:||Maximal chains in the turing degrees|
|Authors:||Chong, C.T. |
|Source:||Chong, C.T., Yu, L. (2007-12). Maximal chains in the turing degrees. Journal of Symbolic Logic 72 (4) : 1219-1227. ScholarBank@NUS Repository. https://doi.org/jsl/1203350783|
|Abstract:||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 α ∈ 2ω,(ω1) L[α] = ω1 if and only if there exists a ∏1 I[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) ∏|1 1 maximal chain of Turing degrees". © 2007. Association for Symbolic Logic.|
|Source Title:||Journal of Symbolic Logic|
|Appears in Collections:||Staff Publications|
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