[Proof Complexity] [Revised preprint] Consistency proof of an arithmetic with substitution inside a bounded arithmetic

[Yoriyuki Yamagata]

My preprint "Consistency proof of an arithmetic with substitution inside a bounded arithmetic" is updated.

http://arxiv.org/abs/1411.7087 

The previous version contains a critical error, so it was withdrawn,  Now I believe that the problem is fixed.  (See the discussion of Section 6).

This paper proves that the system which is obtained from PV by removing induction, but retaining the substitution rule is provably consistent inside S22.  This result strengthens Beckmann's result (Beckmann 2002), albeit that the meta-theory is S22, not S12.

Best,