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

Leszek Aleksander Kołodziejczyk
The Journal of Symbolic Logic
Vol. 71, No. 2 (Jun., 2006), pp. 624-638
Stable URL: http://www.jstor.org/stable/27588470
Page Count: 15
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On the Herbrand Notion of Consistency for Finitely Axiomatizable Fragments of Bounded Arithmetic Theories
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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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