Abstract
The main object of study in this paper is a class of calculi of second-order recursive arithmetic, called ‘calculi of Kind I’. These are very similar to the second-order calculi considered in Tait (1965). The main focus is on questions about ‘translations’ of various sorts between these calculi, and certain other calculi, called ‘calculi of kind II’. These are more like first-order calculi, only with some built-in rules for definition by recursion.
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References
Kleene, S. C .,Introduction to Metamathematics, North-Holland, 1952.
Tait, W. W ., ‘Functional defined by transfinite recursion’, J. of Symbolic Logic 30 (1965), pp. 155–174.
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© 1979 D. Reidel Publishing Company, Dordrecht, Holland
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Svenonius, L. (1979). Two Kinds of Extensions of Primitive Recursive Arithmetic. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds) Essays on Mathematical and Philosophical Logic. Synthese Library, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9825-4_4
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DOI: https://doi.org/10.1007/978-94-009-9825-4_4
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