The importance of Pi01 classes in effective randomness
نویسندگان
چکیده
We prove a number of results in effective randomness, using methods in which Π1 classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.
منابع مشابه
The Importance of Π1 Classes in Effective Randomness
We prove a number of results in effective randomness, using methods in which Π1 classes play an essential role. Amongst many others, the results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.
متن کاملNumberings and Randomness
We prove various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-Löf random left-computably enumerable reals has a Friedberg numbering, as does the family of all Π 1 classes of positive measure. On the other hand, the Π 1 classes contained in the Martin-Löf random reals do not even have an effective numbering, nor ...
متن کاملΠ1 Classes, Peano Arithmetic, Randomness, and Computable Domination
2 Open and Closed Classes in Cantor Space 5 2.1 Open Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Closed Classes . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Compactness Theorem . . . . . . . . . . . . . . . . . . . 7 2.4 Notation For Trees . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Effective Compactness Theorem . . . . . . . . . . . . . . . . . 8
متن کاملTESTING FOR “RANDOMNESS” IN SPATIAL POINT PATTERNS, USING TEST STATISTICS BASED ON ONE-DIMENSIONAL INTER-EVENT DISTANCES
To test for “randomness” in spatial point patterns, we propose two test statistics that are obtained by “reducing” two-dimensional point patterns to the one-dimensional one. Also the exact and asymptotic distribution of these statistics are drawn.
متن کاملDevelopment of monoclonal-antibody-ELISA and -DIP-STICK immunoassays for Penicillium islandicum in rice grains.
Monoclonal antibodies (mAbs) were raised against Penicillium islandicum, a fungus commonly isolated from stored rice grains in South-East Asia. Mice were immunized by a direct, simple method; fresh cell-free surface washings from a solid agar slant culture were injected directly into the peritoneum without prior concentration. Hybridoma supernatants were screened by ELISA. Most of the mAbs rais...
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:
- J. Symb. Log.
دوره 75 شماره
صفحات -
تاریخ انتشار 2010