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March 2012 Domination, forcing, array nonrecursiveness and relative recursive enumerability
Mingzhong Cai, Richard A. Shore
J. Symbolic Logic 77(1): 33-48 (March 2012). DOI: 10.2178/jsl/1327068690

Abstract

We present some abstract theorems showing how domination properties equivalent to being $\overline{GL}_2$ or array nonrecursive can be used to construct sets generic for different notions of forcing. These theorems are then applied to give simple proofs of some known results. We also give a direct uniform proof of a recent result of Ambos-Spies, Ding, Wang and Yu [2009] that every degree above any in $\overline{GL}_2$ is recursively enumerable in a 1-generic degree strictly below it. Our major new result is that every array nonrecursive degree is r.e. in some degree strictly below it. Our analysis of array nonrecursiveness and construction of generic sequences below $\mathbf{ANR}$ degrees also reveal a new level of uniformity in these types of results.

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Mingzhong Cai. Richard A. Shore. "Domination, forcing, array nonrecursiveness and relative recursive enumerability." J. Symbolic Logic 77 (1) 33 - 48, March 2012. https://doi.org/10.2178/jsl/1327068690

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1269.03045
MathSciNet: MR2951628
Digital Object Identifier: 10.2178/jsl/1327068690

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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