Computation theories: An axiomatic approach to recursion on general structures

This is a brief survey of an axiomatic approach to generalized recursion theory. It is based on a set of lectures to the Kiel Summer Institute in Logic 1974. A first report on the project was given in [6]. An axiomatic study is to a large extent an analysis of existing methods and results. Our debts to those who have worked on general recursion theory is therefore considerable, as the many references to follow will bear witness to. A particular debt is due to Johan Moldestad and Dag Normann who have with great enthusiasm participated in the various investigations reported on in this survey.

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