A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings

This paper concerns a constructive adaptation of the classical Borel-Cantelli lemma which allows us to solve such decomposition problems as: when does there exist an infinite object that is decomposable into infinitely many parts that are maximally complex? A constructive proof is supplied of the key theorem and its degree is characterized. For completeness… CONTINUE READING