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- W4239025295 abstract "This chapter provides an introduction to inductive definitions. Mathematical Logic is certainly permeated with inductive definitions. The chapter discusses some examples of concepts which are usually or readily defined in this way. Several methods which have been used to investigate certain particular classes of inductive definitions are also discussed. The chapter describes the method of semantic tableau which may have significant uses. The results about ∏1 positive inductive definitions are new; but it is not clear if that class is significant. The chapter presents several efforts made to present Kleene's theory of recursion in a type 2 object as a branch of inductive theory. Some successful efforts provide a clear indication of how to set up the theory for structures other than the natural numbers. Some inconclusive discussion of the contrary case is also presented. The chapter investigates the forms of inductive definition which occur in proof theory." @default.
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- W4239025295 date "1974-01-01" @default.
- W4239025295 modified "2023-09-27" @default.
- W4239025295 title "Inductive Definitions" @default.
- W4239025295 doi "https://doi.org/10.1016/s0049-237x(08)70591-3" @default.
- W4239025295 hasPublicationYear "1974" @default.
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