Abstract
In this paper the r.e. inseparability and the effective r.e. inseparability of index sets under certain indexings of the computable elements of an effective cpo are studied. As a consequence of the main result on effective r.e. inseparability we obtain a generalization of a theorem by McNaughton. As a further application we obtain generalizations of results by Myhill/Dekker on the productivity of certain index sets. From this we infer the generalization of theorems by Rice/Shapiro/McNaughton/Myhill and Myhill/Shepherdson. This demonstrates the importance of the r.e. inseparability notion.
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Spreen, D. (1984). On r.e. inseparability of CPO index sets. In: Börger, E., Hasenjaeger, G., Rödding, D. (eds) Logic and Machines: Decision Problems and Complexity. LaM 1983. Lecture Notes in Computer Science, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13331-3_36
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DOI: https://doi.org/10.1007/3-540-13331-3_36
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