Degrees of random sets

Degrees of random sets (1991)

by Steven M. Kautz

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Datum	Value	Source
TITLE	Degrees of random sets	INFERENCE
AUTHOR NAME	Steven M. Kautz	user correction
ABSTRACT	An explicit recursion-theoretic definition of a random sequence or random set of natural numbers was given by Martin-Löf in 1966. Other approaches leading to the notions of n-randomness and weak n-randomness have been presented by Solovay, Chaitin, and Kurtz. We investigate the properties of n-random and weakly n-random sequences with an emphasis on the structure of their Turing degrees. After an introduction and summary, in Chapter II we present several equivalent definitions of n-randomness and weak n-randomness including a new definition in terms of a forcing relation analogous to the characterization of n-generic sequences in terms of Cohen forcing. We also prove that, as conjectured by Kurtz, weak nrandomness is indeed strictly weaker than n-randomness. Chapter III is concerned with intrinsic properties of n-random sequences. The main results are that an (n + 1)-random sequence A satisfies the condition A (n) ≡T A⊕0 (n) (strengthening a result due originally to Sacks) and that n-random sequences satisfy a number of strong independence properties, e.g., if A ⊕ B is n-random then A is n-random relative to B. It follows that any countable distributive lattice can be embedded	SVM HeaderParse 0.2
YEAR	1991	SVM HeaderParse 0.2
VENUE TYPE	TECHREPORT	INFERENCE
TECH	PhD Thesis	INFERENCE
CITATIONS	36 found	ParsCit 1.0