The strength of sharply bounded induction

نویسنده

  • Emil Jerábek
چکیده

We prove that the sharply bounded arithmetic T 0 2 in a language containing the function symbol ⌊ x 2y ⌋ (often denoted by MSP) is equivalent to PV1.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Independence results for variants of sharply bounded induction

The theory T 0 2 , axiomatized by the induction scheme for sharply bounded formulas in Buss’ original language of bounded arithmetic (with bx/2c but not bx/2yc), has recently been unconditionally separated from full bounded arithmetic S2. The method used to prove the separation is reminiscent of those known from the study of open

متن کامل

A Remark on Independence Results for Sharply Bounded Arithmetic

The purpose of this note is to show that the independence results for sharply bounded arithmetic of Takeuti 4] and Tada and Tatsuta 3] can be obtained and, in case of the latter, improved by the model-theoretic method developed by the author in 2]. By sharply bounded arithmetic we understand fragments of the theory S 1 2 of Bounded Arithmetic of Buss 1] given by the quantiier-free BASIC axioms ...

متن کامل

Alternative approaches to obtain t-norms and t-conorms on bounded lattices

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

متن کامل

The strength of sharply bounded induction requires MSP

We show that the arithmetical theory T 0 2 +Σ̂ b 1-IND |x|5 , formalized in the language of Buss, i.e. with bx/2c but without the MSP function bx/2yc, does not prove that every nontrivial divisor of a power of 2 is even. It follows that this theory proves neither NP = coNP nor S0 2 . Some arithmetical theories are not merely weak but very weak, in the sense that they do not prove some very basic...

متن کامل

Cuts and overspill properties in models of bounded arithmetic

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 particula...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Math. Log. Q.

دوره 52  شماره 

صفحات  -

تاریخ انتشار 2006