Abstract
This paper studies the degrees of weakly computable reals. It is shown that certain types of limit-recursive reals are Turing incomparable to all weakly computable reals except the recursive and complete ones. Furthermore, it is shown that an r.e. Turing degree is array-recursive iff every real in it is weakly computable.
F. Stephan is supported in part by NUS grant number R252–000–212–112. G. Wu is partially supported by the Start-up grant number M48110008 from Nanyang Technological University and International Collaboration grant number 60310213 of NSFC from China.
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Ng, K.M., Stephan, F., Wu, G. (2006). Degrees of Weakly Computable Reals. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_43
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DOI: https://doi.org/10.1007/11780342_43
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