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- W1822635159 abstract "This chapter provides an introduction to a theory of monotone inductive schemata over arbitrary structures, which is proposed as a natural conceptual framework for generalized recursion theory (g.r.t.). Some examples are presented, with particular attention to recursion on the structure n of functionals of finite type over the natural numbers N. In contrast, higher-type structures are regarded as just further examples, which are the subjects of the notions of g.r.t. rather than tools to explain the notions. The theory Ind( n ) provided by inductive schemata turns out in this case to be equivalent to that given by Kleene's schemata. The approach to g.r.t. via inductive schemata is compared with the axiomatic enumerative approach. A generalized notion of finiteness enters naturally in connection with so-called stage comparison theorems. The chapter presents the recursion on structures of continuous functionals over n ." @default.
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- W1822635159 date "1977-01-01" @default.
- W1822635159 modified "2023-10-17" @default.
- W1822635159 title "Inductive Schemata and Recursively Continuous Functionals" @default.
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- W1822635159 doi "https://doi.org/10.1016/s0049-237x(09)70435-5" @default.
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