A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings
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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.
KeywordsComputational Mathematic Constructive Proof Decomposition Problem Constructive Adaptation Constructive Generalization
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