Herbrand's theorem and term induction

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Archive for Mathematical Logic 45 (4):447-503 (2006)
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Abstract

We study the formal first order system TIND in the standard language of Gentzen's LK . TIND extends LK by the purely logical rule of term-induction, that is a restricted induction principle, deriving numerals instead of arbitrary terms. This rule may be conceived as the logical image of full induction.

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2005

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10.1007/s00153-005-0327-6

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Sets of theorems with short proofs.Daniel Richardson - 1974 - Journal of Symbolic Logic 39 (2):235-242.
Cut normal forms and proof complexity.Matthias Baaz & Alexander Leitsch - 1999 - Annals of Pure and Applied Logic 97 (1-3):127-177.
Generalizing theorems in real closed fields.Matthias Baaz & Richard Zach - 1995 - Annals of Pure and Applied Logic 75 (1-2):3-23.
Some results on speed-up.Tsuyoshi Yukami - 1984 - Annals of the Japan Association for Philosophy of Science 6 (4):195-205.

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