Abstract
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 a classical (i.e., nonconstructive) proof is also provided.
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This research was supported in part by NSF Grants MCS78-81486 and MCS77-28305, and was also facilitated by the use of Theory Net, NSF Grant No. MCS78-01689.
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DeMillo, R.A., Lipton, R.J. A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings. Math. Systems Theory 13, 95–104 (1979). https://doi.org/10.1007/BF01744291
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DOI: https://doi.org/10.1007/BF01744291