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June 2009 Automorphisms of the truth-table degrees are fixed on a cone
Bernard A. Anderson
J. Symbolic Logic 74(2): 679-688 (June 2009). DOI: 10.2178/jsl/1243948334

Abstract

Let Dtt denote the set of truth-table degrees. A bijection π : Dtt → Dtt is an automorphism if for all truth-table degrees x and y we have x ≤tt y ⇔ π (x) ≤tt π (y). We say an automorphism π is fixed on a cone if there is a degree b such that for all x ≥tt b we have π (x) = x. We first prove that for every 2-generic real X we have X'≰tt X ⊕ 0'. We next prove that for every real X ≥tt 0' there is a real Y such that Y ⊕ 0' ≡tt Y' ≡tt X. Finally, we use this to demonstrate that every automorphism of the truth-table degrees is fixed on a cone.

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Bernard A. Anderson. "Automorphisms of the truth-table degrees are fixed on a cone." J. Symbolic Logic 74 (2) 679 - 688, June 2009. https://doi.org/10.2178/jsl/1243948334

Information

Published: June 2009
First available in Project Euclid: 2 June 2009

zbMATH: 1165.03019
MathSciNet: MR2518818
Digital Object Identifier: 10.2178/jsl/1243948334

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 2 • June 2009
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