On Splits of Computably enumerable sets

Peter Cholak

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arXiv · 1605.03034

On Splits of Computably enumerable sets

Peter Cholak

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Abstract

Our focus will be on the computably enumerable (c.e.) sets and trivial, non-trivial, Friedberg, and non-Friedberg splits of the c.e. sets. Every non-computable set has a non-trivial Friedberg split. Moreover, this theorem is uniform. V. Yu. Shavrukov recently answered the question which c.e. sets have a non-trivial non-Friedberg splitting and we provide a different proof of his result. We end by showing there is no uniform splitting of all c.e. sets such that all non-computable sets are non-trivially split and, in addition, all sets with a non-trivial non-Friedberg split are split accordingly.

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BibTeX RIS

Peter Cholak. 2016-08-08. On Splits of Computably enumerable sets. https://arxiv.org/abs/1605.03034

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