The finite intersection principle and genericity

DOI10.1017/S0305004115000651zbMath1375.03046MaRDI QIDQ5360372

Noam Greenberg, Dan Turetsky, David E. Diamondstone, Rodney G. Downey

Publication date: 28 September 2017

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

computability1-generic setTuring degreegeneric setfinite intersection2IP degreeFIP degree

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Other Turing degree structures (03D28)

Related Items (3)

Dominating the Erdős-Moser theorem in reverse mathematics ⋮ Any FIP real computes a 1-generic ⋮ Degrees bounding principles and universal instances in reverse mathematics

Cites Work

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• On the strength of the finite intersection principle
• Embedding and coding below a 1-generic degree
• Weak comparability of well orderings and reverse mathematics
• A characterization of the entropies of multidimensional shifts of finite type
• Countable algebra and set existence axioms
• The atomic model theorem and type omitting
• The canonical Ramsey theorem and computability theory

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