\(\Pi_1^0\) classes, Peano arithmetic, randomness, and computable domination

DOI10.1215/00294527-2010-009zbMath1197.03045OpenAlexW1970107198MaRDI QIDQ976541

Damir D. Dzhafarov, David E. Diamondstone, Robert I. Soare

Publication date: 11 June 2010

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/00294527-2010-009

zbMATH Keywords

survey paperPeano arithmeticrandomness\(\Pi^0_1\) classesbasis theoremscomputable dominationhyperimmunity

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62) Recursively (computably) enumerable sets and degrees (03D25) Other degrees and reducibilities in computability and recursion theory (03D30) Algorithmic randomness and dimension (03D32)

Related Items (7)

An effectively closed set with no join property* ⋮ Antibasis theorems for \({\Pi^0_1}\) classes and the jump hierarchy ⋮ choice classes ⋮ On the cardinality of future worldlines in discrete spacetime structures ⋮ COMPUTABLY COMPACT METRIC SPACES ⋮ Computability of Subsets of Metric Spaces ⋮ Randomness below complete theories of arithmetic

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