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Arithmetical Sacks Forcing

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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.

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Author information

Authors and Affiliations

  1. School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, Wellington, New Zealand

    Rod Downey

  2. Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore, 117543, Singapore

    Liang Yu

Authors
  1. Rod Downey
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  2. Liang Yu
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Corresponding author

Correspondence to Rod Downey.

Additional information

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.

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Downey, R., Yu, L. Arithmetical Sacks Forcing. Arch. Math. Logic 45, 715–720 (2006). https://doi.org/10.1007/s00153-006-0004-4

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  • DOI: https://doi.org/10.1007/s00153-006-0004-4

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