Fragments of arithmetic
نویسندگان
چکیده
منابع مشابه
Predicative fragments of Frege Arithmetic
Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity in...
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This paper deals with the weak fragments of arithmetic PV and S\ and their induction-free fragments PV and S^ • We improve the bootstrapping of 5^, which allows us to show that the theory S\ can be axiomatized by the set of axioms BASIC together with any of the following induction schemas: Y,\-PIND, Y,\-LIND, H^PINDOT U\-LIND. We improve prior results of Pudlak, Buss and Takeuti establishing th...
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We give combinatorial and computational characterizations of the NP search problems definable in the bounded arithmetic theories T 2 2 and T 3 2 . By a search problem in full generality we mean simply a binary relation R(x, y) such that ∀x∃yR(x, y) holds. The search task is: given an instance x find a solution y such that R(x, y) holds. The most important class of search problems are NP search ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1985
ISSN: 0168-0072
DOI: 10.1016/0168-0072(85)90030-2