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RANDOMNESS VIA INFINITE COMPUTATION AND EFFECTIVE DESCRIPTIVE SET THEORY.

The article discusses randomness via infinite computation and effective descriptive set theory. It discusses a study on randomness beyond Π11-randomness and its Martin-Löf type variant. It focuses on a class strictly between Π1 1 and Σ1 2 that is given by the infinite time Turing machines (ITTMs). R...

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Publicado en:Journal of Symbolic Logic Vol. 83; no. 2; pp. 766 - 790
Autores principales: CARL, MERLIN, SCHLICHT, PHILIPP
Formato: Artículo
Publicado: Cambridge University Press Jun2018
Materias:
Computational statistics
Set theory
Random numbers
Turing machines
Martingales (Mathematics)
Mathematics theorems
Acceso en línea:Ver este registro en EBSCOhost
Sumario:The article discusses randomness via infinite computation and effective descriptive set theory. It discusses a study on randomness beyond Π11-randomness and its Martin-Löf type variant. It focuses on a class strictly between Π1 1 and Σ1 2 that is given by the infinite time Turing machines (ITTMs). Results include mutual randoms not sharing information and that a version of van Lambalgen's theorem holds, and an analogue to a theorem of Sacks.