From bi-immunity to absolute undecidability

  title={From bi-immunity to absolute undecidability},
  author={Laurent Bienvenu and Adam R. Day and Rupert H{\"o}lzl},
  journal={J. Symb. Log.},
An infinite binary sequence A is absolutely undecidable if it is impossible to compute A on a set of positions of positive upper density. Absolute undecidability is a weakening of bi-immunity. Downey, Jockusch and Schupp [2] asked whether, unlike the case for bi-immunity, there is an absolutely undecidable set in every non-zero Turing degree. We provide a positive answer to this question by applying techniques from coding theory. We show how to use Walsh-Hadamard codes to build a truth-table… CONTINUE READING