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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Baaz, M., Moser, G. Herbrand's theorem and term induction. Arch. Math. Logic 45, 447–503 (2006). https://doi.org/10.1007/s00153-005-0327-6
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DOI: https://doi.org/10.1007/s00153-005-0327-6