Closed left-R.E. sets

Authors:
Sanjay Jain;Frank Stephan;Jason Teutsch
Affiliations:
Department of Computer Science, National University of Singapore, Singapore, Republic of Singapore;Department of Computer Science, National University of Singapore, Singapore, Republic of Singapore and Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore;Institut für Informatik, Universität Heidelberg, Heidelberg, Germany
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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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 manyone 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.