Totality in applicative theories
نویسندگان
چکیده
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 کامل[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...
متن کاملChoice 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 generalize this to TAPP + inductive definitions. Finally, we use TAPP to show that P.Martin-Lofs basic extensional theory MLp is conservative over intuitionistic arithmetic. 1980 Mathematical Subject Classification: 03F50,...
متن کاملTruth in Applicative Theories
We give a survey on truth theories for applicative theories. It comprises Frege structures, Universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.
متن کاملApplicative Theories and Explicit Mathematics
[5] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [6] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [9] Susumu Hayashi and Satoshi Kobayashi. A new formulation of Feferman's system of functions and classes and its relation to Frege structures.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1995
ISSN: 0168-0072
DOI: 10.1016/0168-0072(94)00037-4