New PDF release: Algorithms for Diophantine Equations [PhD Thesis]

By de Weger B.M.M.

ISBN-10: 9061963753

ISBN-13: 9789061963752

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Extra resources for Algorithms for Diophantine Equations [PhD Thesis]

Example text

Then the problem comes down to the fact that it may be the case that every x is such that (x) if and only if tf;(x), but it is not knowable that that is the case. This problem would not arise if everything true were knowable in principle. In that case two specifiable and equal sets would be known to be equal, in principle. But in that case, knowability in principle would coincide with truth, and we would be adding nothing to classical mathematics. The formula D would be equivalent to .

Pp. 158-176. [19] Randolph, J. : 1968, Basic Real and Abstract Analysis, Academic Press, New York. : 1967 , Theory of Recursive Functions and Effective Computability , McGraw-Hill, New York. : 1968, Introduction to Analysis, Scott, Foresman, Glenview, III. : 'On Church's Thesis' , Typescript. : 1984, 'Epistemic Arit~metic and Intuitionistic Arithmetic', to appear in S. ), Intensional Mathematics, North-Holland Pub. , New York. [24] Shelah, S. : 1979, 'On Well Ordering and More on Whitehead's Problem', Abstract 79T-E47, Notices Amer.

INTRODUCTION Computable Kripke closures are properties of relations which have closures in, roughly speaking, the sense of the transitive closure. They were introduced in [8] to generalize Kripke-style tableaux constructions and were studied from a model-theoretic perspective by Weaver and Gumb [19]. In section 1 of this paper, we review the properties of computable Kripke closures. In section 2, we state four additional laws that can be imposed on computable Kripke closures and state properties of the closures determined by these laws.

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Algorithms for Diophantine Equations [PhD Thesis] by de Weger B.M.M.

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