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Domination, forcing, array nonrecursiveness and relative recursive enumerability
Journal of Symbolic Logic (JSL)
We present some abstract theorems showing how domination properties equivalent to being 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  that every degree above any in is recursively enumerable in a 1-generic degree strictly below it. Our major new result is that every arraydoi:10.2178/jsl/1327068690 fatcat:6cdo34ugorg73d3yiffyfe3cxq