Retracts of numerations☆

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Abstract

In this paper we study some important properties of numerations such as precompleteness, acceptability, etc. which can be passed on to their retracts. Furthermore we show a necessary and sufficient condition for a category Ret(α) of retracts of a numeration α and morphisms to be normal effectively Cartesian closed, in terms of α. We also study some examples of such numeration-theoretic retract calculus.

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This research was carried out when the author was at Copenhagen University. Also this research was supported by Canada Natural Science and Engineering Research Council grant A2457. The author thanks the referee who gave very valuable suggestions.

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