Hilbert's tenth problem for weak theories of arithmetic

Annals of Pure and Applied Logic 61 (1-2):63-73 (1993)
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Abstract

Hilbert's tenth problem for a theory T asks if there is an algorithm which decides for a given polynomial p() from [] whether p() has a root in some model of T. We examine some of the model-theoretic consequences that an affirmative answer would have in cases such as T = Open Induction and others, and apply these methods by providing a negative answer in the cases when T is some particular finite fragment of the weak theories IE1 or IU-1

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10.1016/0168-0072(93)90198-m

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Citations of this work

Division by zero.Emil Jeřábek - 2016 - Archive for Mathematical Logic 55 (7-8):997-1013.

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References found in this work

Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
Bounded existential induction.George Wilmers - 1985 - Journal of Symbolic Logic 50 (1):72-90.
Diophantine Induction.Richard Kaye - 1990 - Annals of Pure and Applied Logic 46 (1):1-40.
Parameter‐Free Universal Induction.Richard Kaye - 1989 - Mathematical Logic Quarterly 35 (5):443-456.

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