15-317 Constructive Logic
Lecture 10: Cut Elimination

In this lecture we prove one of the central theorems in logic, namely that cut is admissible in the cut-free sequent calculus. This completes the connection between truth (as defined by natural deduction) and sequent calculus with numerous important corollaries about truth, expressed in the previous lecture as properties of the sequent calculus.

• Reading: 10-cutelim.pdf
• Key concepts:
  • Cut formula
  • Cut theorem
  • Nested induction
  • Cut elimination
  • Sequent calculus for quantifiers
• Previous lecture: Sequent Calculus
• Next lecture: Inversion

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Frank Pfenning