A Note on the Proof-Theoretic Strength of a Single Application of the Schema of Identity

  • Authors:

  • Matthias Baaz;Christian G. Fermüller

  • Affiliations:

  • -;-

  • Venue:
  • PTCS '01 Proceedings of the International Seminar on Proof Theory in Computer Science
  • Year:
  • 2001

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Abstract

Every instance of the schema of identity is derivable from identity axioms. However, from a proof theoretic perspective the schema of identity is quite powerful. Even one instance of it can be used to prove formulas uniformly where no fixed number of instances of identity axioms is sufficient for this purpose.