The importance of Π10 classes in effective randomness

DOI10.2178/jsl/1264433928zbMath1184.03039OpenAlexW2164699156MaRDI QIDQ5190208

Andrew E. M. Lewis, George Barmpalias, Keng Meng Ng

Publication date: 15 March 2010

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1264433928

zbMATH Keywords

Peano arithmeticMartin-Löf randomnessTuring degrees\(\Pi^0_1\)-classes\(K\)-trivialsLR degrees

Mathematics Subject Classification ID

Other Turing degree structures (03D28) Algorithmic randomness and dimension (03D32)

Related Items (13)

Randomness, Computation and Mathematics ⋮ Propagation of partial randomness ⋮ Depth, Highness and DNR Degrees ⋮ Low upper bounds in the LR degrees ⋮ Relativized depth ⋮ Growth and irreducibility in path-incompressible trees ⋮ Computability theory. Abstracts from the workshop held April 25 -- May 1, 2021 (hybrid meeting) ⋮ Effective Bi-immunity and Randomness ⋮ A HIERARCHY OF COMPUTABLY ENUMERABLE DEGREES ⋮ Lowness for Demuth Randomness ⋮ Highness properties close to PA completeness ⋮ A computable analysis of majorizing martingales ⋮ Randomness below complete theories of arithmetic

Cites Work

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• Degrees of members of \(\Pi_ 1^ 0\) classes
• Lowness properties and randomness
• RELATIVIZING CHAITIN'S HALTING PROBABILITY
• Calibrating Randomness
• Non-cupping and randomness
• MASS PROBLEMS AND HYPERARITHMETICITY
• Decidability of the “almost all” theory of degrees
• Almost everywhere domination and superhighness
• Low for random reals and positive-measure domination
• Degrees of Unsolvability. (AM-55)
• The definition of random sequences
• Class groups of integral group rings

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