منابع مشابه
Classical 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...
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In this paper, we describe improvements to the function field sieve (FFS) for the discrete logarithm problem in Fpn , when p is small. Our main contribution is a new way to build the algebraic function fields needed in the algorithm. With this new construction, the heuristic complexity is as good as the complexity of the construction proposed by Adleman and Huang [2], i.e Lpn [1/3, c] = exp((c ...
متن کاملThe computational content of classical arithmetic
Almost from the inception of Hilbert’s program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various methods of extracting computational information from proofs in classical first-order arithmetic, and reflects on some of the relationships between them. Variants ...
متن کاملA Realizability Interpretation for Classical Arithmetic
A constructive realizablity interpretation for classical arithmetic is presented, enabling one to extract witnessing terms from proofs of 1 sentences. The interpretation is shown to coincide with modified realizability, under a novel translation of classical logic to intuitionistic logic, followed by the Friedman-Dragalin translation. On the other hand, a natural set of reductions for classical...
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...
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ژورنال
عنوان ژورنال: Logic and Logical Philosophy
سال: 2003
ISSN: 1425-3305
DOI: 10.12775/llp.2003.012