1998
DOI: 10.1007/bfb0028594
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Abstract: Abstract. A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay 23 and Chaitin 10 we s a y that an r.e. real dominates an r.e. real if from a good approximation of from below one can compute a good approximation of from below. We shall study this relation and characterize it in terms of relations between r.e. sets. Solovay's 23 -like numbers are the maximal r.e. real numbers with respect to this order. They are random r.e. rea… Show more

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Cited by 66 publications
(116 citation statements)
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References 16 publications
(2 reference statements)
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“…Оказывается, что класс таких чисел имеет несколько эквивалентных описаний [17,70]. Мы приведём их, следуя [84].…”
Section: Ks (( ) )unclassified
See 1 more Smart Citation
“…Оказывается, что класс таких чисел имеет несколько эквивалентных описаний [17,70]. Мы приведём их, следуя [84].…”
Section: Ks (( ) )unclassified
“…Оказывается, что полные по Соловею числа и только они могут появляться как «число˙» в описанной выше конструкции [161,17]. Числа типа˙имеют и ещё одно описание (помимо полноты по Соловею): это в точности перечислимые снизу случайные числа в интервале (0, 1).…”
Section: монотонная и априорная сложности и случайностьunclassified
“…Calude et al [2] sharpened Theorem 1.14 as follows. Theorem 1.15 (Calude et al [2]). If α is Ω-like, then α is an Ω-number.…”
Section: (Solovay [18])mentioning
confidence: 99%
“…Thus, every Ω-like number is an Ω-number. Calude et al [2] posed the natural question, "Is every recursively enumerable random real an Ω-number?" In Theorem 2.1, we show that every recursively enumerable random real is Ω-like and conclude from Theorem 1.15 that the answer to this question is yes.…”
Section: (Solovay [18])mentioning
confidence: 99%
“…reals has grown into a significant part of modern algorithmic randomness, and is best presented in [DH10, Chapters 5 and 9]. The present section is an original presentation of some facts regarding Martin-Löf random reals that stem from [Sol75,CHKW01,KS01] and are further elaborated on in [DHN02], which are essential for the proof of Theorem 1.1. Moreover, some of these facts are not given explicitly in the sources above, but can be recovered from the proofs.…”
Section: Overview Of Martin-löf Random Left-ce Realsmentioning
confidence: 99%