Totality in Applicative Theories
نویسندگان
چکیده
In this paper we study applicative theories of operations and numbers with (and without) the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system ((0 1-CA) <"0 of second order arithmetic. Essential use will be made of so-called xed-point theories with ordinals, certain innnitary term models and Church Rosser properties.
منابع مشابه
[To appear in: Annals of Pure and Applied Logic] Totality in applicative theories
In this paper we study applicative theories of operations and numbers with (and without) the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system ( 0 1 -CA) <" 0 of second order arithmetic. Essential use will be made of so-called...
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عنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 74 شماره
صفحات -
تاریخ انتشار 1995