Lowness for Weak Genericity and Randomness
نویسندگان
چکیده
We prove that lowness for weak genericity is equivalent to semicomputable traceability which is strictly between hyperimmune-freeness and computable traceability. We also show that semi-computable traceability implies lowness for weak randomness. These results refute a conjecture raised by several people.
منابع مشابه
Lowness for Kurtz randomness
We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are ...
متن کاملLowness and Π 02
We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.
متن کاملLowness and Π2 Nullsets
We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.
متن کاملCharacterizing Lowness for Demuth Randomness
We show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [14] (also Problem 5.5.19 in [33]). We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also sho...
متن کاملω-Change Randomness and Weak Demuth Randomness
We extend our work on difference randomness. Each component of a difference test is a Boolean combination of two r.e. open sets; here we consider tests in which the k component is a Boolean combination of g(k) r.e. open sets for a given recursive function g. We use this method to produce an alternate characterization of weak Demuth randomness in terms of these tests and further show that a real...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005