Robin Hirsch's articles on Proof Theory.

• R. Hirsch, I. Hodkinson and R. Maddux. On the number of variables required for proofs.
  In the Journal of Symbolic Logic , volume 67, number 1, pp 197--213, 2002.
  
• R. Hirsch, I. Hodkinson and R. Maddux. Provability with finitely many variables.
  In the Bulletin of Symbolic Logic, volume 8, number 3, pp 348-379, 2002