Genericity for Mathias forcing over general Turing ideals

DOI10.1007/s11856-016-1420-8zbMath1377.03031arXiv1505.02226OpenAlexW2962795890MaRDI QIDQ503254

Peter A. Cholak, Damir D. Dzhafarov, Mariya Ivanova Soskova

Publication date: 11 January 2017

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.02226

zbMATH Keywords

recursion theorycomputable Mathias forcingTuring ideals

Mathematics Subject Classification ID

Applications of set theory (03E75) Other aspects of forcing and Boolean-valued models (03E40) Other Turing degree structures (03D28) Algorithmic randomness and dimension (03D32)

Related Items (2)

The uniform content of partial and linear orders ⋮ Ramsey’s theorem for singletons and strong computable reducibility

Cites Work

• On degrees of recursive unsolvability
• Upward closure and cohesive degrees
• On the strength of Ramsey's theorem
• A variant of Mathias forcing that preserves \(\mathsf{ACA}_0\)
• Generics for computable Mathias forcing
• The upper semi-lattice of degrees of recursive unsolvability
• On the strength of Ramsey's theorem for pairs
• Turing Computability
• Ramsey's theorem and cone avoidance
• Happy families
• Hyperarithmetically Encodable Sets
• On a conjecture of Dobrinen and Simpson concerning almost everywhere domination
• Uniformly introreducible sets
• Sets with no subset of higher degree

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