[To appear in: Annals of Pure and Applied Logic] 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 in nitary term models and Church Rosser properties.
منابع مشابه
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 x...
متن کاملA feasible theory of truth over combinatory algebra
We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that hav...
متن کاملThe Suslin operator in applicative theories: Its proof-theoretic analysis via ordinal theories
The Suslin operator E1 is a type-2 functional testing for the wellfoundedness of binary relations on the natural numbers. In the context of applicative theories, its proof-theoretic strength has been analyzed in Jäger and Strahm [18]. This article provides a more direct approach to the computation of the upper bounds in question. Several theories featuring the Suslin operator are embedded into ...
متن کاملExtended Bar Induction in Applicative Theories
TAPP is a total applicative theory, conservative over intuitionistic arithmetic. In this paper, we first show that the same holds for TAPP + the choice principle EAC; then we extend TAPP with choice sequences and study the principle EBIZ (arithmetical extended bar induction of type zero). The resulting theories are used to characterise the arithmetical fragment of EL (elementary intuitionistic ...
متن کاملA new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP
We introduce a version of operational set theory, OST, without a choice operation, which has a machinery for ∆0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke-Platek set theory KP with infinity are pairwise Π1 equivalent. We al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016