On the Herbrand Notion of Consistency for Finitely Axiomatizable Fragments of Bounded Arithmetic Theories

Journal of Symbolic Logic 71 (2):624 - 638 (2006)
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Abstract

Modifying the methods of Z. Adamowicz's paper Herbrand consistency and bounded arithmetic [3] we show that there exists a number n such that ⋃m Sm (the union of the bounded arithmetic theories Sm) does not prove the Herbrand consistency of the finitely axiomatizable theory $S_{3}^{n}$

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Citations of this work

Passive induction and a solution to a Paris–Wilkie open question.Dan E. Willard - 2007 - Annals of Pure and Applied Logic 146 (2-3):124-149.

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References found in this work

On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
On Herbrand consistency in weak arithmetic.Zofia Adamowicz & Paweł Zbierski - 2001 - Archive for Mathematical Logic 40 (6):399-413.

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