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Theories of arithmetic in first-order logic, such as Peano arithmetic, second-order arithmetic, Heyting arithmetic, and their subsystems and extensions. Models of Peano arithmetic.

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Kleene normal form theorem for r.e. relations proven in arithmetical theories

After reading the relevant chapters of Classical Recursion Theory (freely available from here), I have the following questions concerning Theorem II.1.10 (Normal form theorem) and Theorem IV.1.9 (Enum …
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