Absorbing the structural rules in the sequent calculus with additional atomic rules

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Archive for Mathematical Logic 59 (3-4):389-408 (2020)
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Abstract

We show that if the structural rules are admissible over a set \ of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in \ to the multisuccedent minimal and intuitionistic \ calculi as well as to the classical one. Two applications to pure logic and to the sequent calculus with equality are presented.

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10.1007/s00153-019-00696-5

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References found in this work

Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
Mathematical Intuitionism. Introduction to Proof Theory.A. G. Dragalin & E. Mendelson - 1990 - Journal of Symbolic Logic 55 (3):1308-1309.

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