RANK AND RANDOMNESS.

We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α , while ensuring that the sequences that inductively witness R 's rank are all Martin-Löf random with respect to a single coun...

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Detalles Bibliográficos
Publicado en:Journal of Symbolic Logic Vol. 84; no. 4; pp. 1527 - 1544
Autores principales: HÖLZL, RUPERT, PORTER, CHRISTOPHER P.
Formato: Artículo
Publicado: Cambridge University Press Dec2019
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Acceso en línea:Ver este registro en EBSCOhost
Descripción
Sumario:We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α , while ensuring that the sequences that inductively witness R 's rank are all Martin-Löf random with respect to a single countably supported and computable measure. This is a strengthening for random degrees of a recent result of Downey, Wu, and Yang, and can be understood as a randomized version of it.