Cuts and overspill properties in models of bounded arithmetic

Author(s):

Morteza Moniri , S. Hosein Sajjadi

Message:
Abstract:
In this paper we are concerned with cuts in models of Samuel Bus's 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.
Keywords:

Mathematical logic , bounded arithmetic , polynomial induction , cut , overspill , underspill

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:8 Issue: 1, May 2013
Page:
59
https://www.magiran.com/p1111747