TY - JOUR JF - IJMSI JO - IJMSI VL - 8 IS - 1 PY - 2013 Y1 - 2013/5/01 TI - Cuts and overspill properties in models of bounded arithmetic TT - N2 - In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence 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. SP - 59 EP - 66 AU - Moniri, Morteza AU - Sajjadi, S. Hosein AD - KW - Mathematical logic KW - bounded arithmetic KW - polynomial induction KW - cut KW - overspill KW - underspill. UR - http://ijmsi.ir/article-1-403-en.html DO - 10.7508/ijmsi.2013.01.006 ER -