منابع مشابه
Intuitionistic weak arithmetic
We construct ω-framed Kripke models of i∀1 and iΠ1 non of whose worlds satisfies ∀x∃y(x = 2y∨x = 2y+1) and ∀x, y∃zExp(x, y, z) respectively. This will enable us to show that i∀1 does not prove ¬¬∀x∃y(x = 2y ∨ x = 2y + 1) and iΠ1 does not prove ¬¬∀x, y∃zExp(x, y, z). Therefore, i∀1 0 ¬¬lop and iΠ1 0 ¬¬iΣ1. We also prove that HA 0 lΣ1 and present some remarks about iΠ2. 2000 Mathematics Subject C...
متن کاملIndependence results for weak systems of intuitionistic arithmetic
This paper proves some independence results for weak fragments of Heyting arithmetic by using Kripke models. We present a necessary condition for linear Kripke models of arithmetical theories which are closed under the negative translation and use it to show that the union of the worlds in any linear Kripke model of HA satisfies PA. We construct a two-node PA-normal Kripke structure which does ...
متن کاملClassical arithmetic is part of intuitionistic arithmetic
One of Michael Dummett’s most striking contributions to the philosophy of mathematics is an argument to show that the correct logic to apply in mathematical reasoning is not classical but intuitionistic. In this article I wish to cast doubt on Dummett’s conclusion by outlining an alternative, motivated by consideration of a well-known result of Kurt Gödel, to the standard view of the relationsh...
متن کاملClassical and Intuitionistic Models of Arithmetic
Given a classical theory T, a Kripke structure K = (K,≤, (Aα)α∈K ) is called T-normal (or locally T) if for each α ∈ K, Aα is a classical model of T. It has been known for some time now, thanks to van Dalen, Mulder, Krabbe, and Visser, that Kripke models of HA over finite frames (K,≤) are locally PA. They also proved that models of HA over the frame (ω,≤) contain infinitely many Peano nodes. We...
متن کاملA Note on Bootstrapping Intuitionistic Bounded Arithmetic
This paper, firstly, discusses the relationship between Buss’s definition and Cook and Urquhart’s definition of BASIC axioms and of IS 2 . The two definitions of BASIC axioms are not equivalent; however, each intuitionistically implies the law of the excluded middle for quantifier-free formulas. There is an elementary proof that the definitions of IS 2 are equivalent which is not based on reali...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2003
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-003-0189-8