ω-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 th 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 alter...
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| Main Authors: | , |
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| 格式: | Article |
| 語言: | English |
| 出版: |
2015
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| 在線閱讀: | https://hdl.handle.net/10356/107191 http://hdl.handle.net/10220/25391 |
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| 機構: | Nanyang Technological University |
| 語言: | English |
| 總結: | 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 th 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 is weakly Demuth random if and only if it is Martin-Löf random and cannot compute a strongly prompt r.e. set. We conclude with a study of related lowness notions and obtain as a corollary that lowness for balanced randomness is equivalent to being recursive. |
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