@MISC{Barmpalias_resolutesequences, author = {George Barmpalias and Rod and G. Downey}, title = {RESOLUTE SEQUENCES IN INITIAL SEGMENT COMPLEXITY}, year = {} }

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Abstract

Abstract. We study infinite sequences whose initial segment complexity is invariant under effective insertions of blocks of zeros in-between their digits. Surprisingly, such resolute sequences may have nontrivial initial segment complexity. In fact, we show that they occur in many well known classes from computability theory, e.g. in every jump class and every high degree. Moreover there are degrees which consist entirely of resolute sequences, while there are degrees which do not contain any. Finally we establish connections with the contiguous c.e. degrees, the ultracompressible sequences, the anti-complex sequences thus demonstrating that this class is an interesting superclass of the sequences with trivial initial segment complexity. 1.