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Arithmetical Sacks Forcing |
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| Authors: | Rod Downey Liang Yu |
| Affiliation: | (1) School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, Wellington, New Zealand;(2) Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore, 117543, Singapore |
| Abstract: | We answer a question of Jockusch by constructing a hyperimmune-free minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.The first author was supported in part by the Marsden Fund of New Zealand.The second author was supported by a postdoctoral fellowship from the New Zealand Institute for Mathematics and its Applications, NSF of China No.10471060 and No.10420130638. |
| Keywords: | Sacks forcing Hyperimmune-freeness Minimal degree |
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