Logical strength of complexity theory and a formalization of the PCP   theorem in bounded arithmetic
  We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of the existence and of some properties of the (n,d,{\lambda})-graphs in PV1. 
J\'an Pich (Charles University in Prague)
math.LO cs.CC