%0 Journal Article %A Moniri, Morteza %A Sajjadi, S. Hosein %T Cuts and overspill properties in models of bounded arithmetic %J Iranian Journal of Mathematical Sciences and Informatics %V 8 %N 1 %U http://ijmsi.ir/article-1-403-en.html %R 10.7508/ijmsi.2013.01.006 %D 2013 %K Mathematical logic, bounded arithmetic, polynomial induction, cut, overspill, underspill., %X 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. %> http://ijmsi.ir/article-1-403-en.pdf %P 59-66 %& 59 %! %9 Research paper %L A-10-1-126 %+ %G eng %@ 1735-4463 %[ 2013