Cuts and overspill properties in models of bounded arithmetic
Morteza Moniri, S. Hosein Sajjadi · 2013
In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like S i and T i 2 .I n cor- respondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p- cuts and small cuts. In particular, we prove some overspill and underspill properties for them.