@INPROCEEDINGS{Stephan02martin-löfrandom, author = {Frank Stephan}, title = {Martin-Löf Random and PA-complete Sets}, booktitle = {In [4}, year = {2002}, pages = {341--347} }

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Abstract

A set A is Martin-Lof random iff the class fAg does not have \Sigma 1 -measure 0. A set A is PA-complete if one can compute relative to A a consistent and complete extension of Peano Arithmetic. It is shown that every Martin-Lof random set either permits to solve the halting problem K or is not PA-complete. This result implies a negative answer to the question of Ambos-Spies and Kucera whether there is a Martin-Lof random set not above K which is also PA-complete.