Abstract
My main purpose here is to describe an abstract, algebraic context in which one can develop at least the rudiments of the theory of inductive definability. It will be obvious that all the standard examples of induction fit the abstract model in a natural way: these include ordinary recursion theory on the integers and its generalizations to various kinds of abstract structures as well as the theories of positive and non-monotone elementary induction, e.g. see Moschovakis (1974a, b). Despite this generality, the model is very simple and one can establish for it easily the basic results which are common to all these theories. My hope is that future monographs on inductive definability will start with a brief chapter on ‘algebraic preliminaries’ which will contain some version of this material.
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© 1977 D. Reidel Publishing Company, Dordrecht, Holland
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Moschovakis, Y.N. (1977). On the Basic Notions in the Theory of Induction. In: Butts, R.E., Hintikka, J. (eds) Logic, Foundations of Mathematics, and Computability Theory. The University of Western Ontario Series in Philosophy of Science, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1138-9_12
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DOI: https://doi.org/10.1007/978-94-010-1138-9_12
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