Abstract
A set is called r-closed left-r.e. iff every set r-reducible to it is also a left-r.e. set. It is shown that some but not all left-r.e. cohesive sets are many-one closed left-r.e. sets. Ascending reductions are many-one reductions via an ascending function; left-r.e. cohesive sets are also ascening closed left-r.e. sets. Furthermore, it is shown that there is a weakly 1-generic many-one closed left-r.e. set.
S. Jain has been supported in part by NUS grants C252-000-087-001 and R252-000-420-112; F. Stephan has been supported in part by NUS grant R252-000-420-112; J. Teutsch has been supported by the Deutsche Forschungsgemeinschaft grant ME 1806/3-1.
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Jain, S., Stephan, F., Teutsch, J. (2011). Closed Left-R.E. Sets. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_23
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DOI: https://doi.org/10.1007/978-3-642-20877-5_23
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