Chapters on Bounded Arithmetic
نویسنده
چکیده
We characterize the collapse of Buss’ bounded arithmetic in terms of the prov able collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.
منابع مشابه
Chapters on Bounded Arithmetic
We characterize the collapse of Buss bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general 1nodel theoretical investigations on fragments of bounded arithmetic.
متن کاملCuts 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 کاملPolynomial Arithmetic 3
(1) Many typos have been corrected (2) Some redoundancy has been eliminated Notes on polynomially bounded arithmetic Abstract We characterize the collapse of Buss' bounded arithmetic in terms of the prov-able collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.
متن کاملProofs, Programs and Abstract Complexity
Axiom systems are ubiquitous in mathematical logic, one famous and well studied example being first order Peano arithmetic. Foundational questions asked about axiom systems comprise analysing their provable consequences, describing their class of provable recursive functions (i.e. for which programs can termination be proven from the axioms), and characterising their consistency strength. One b...
متن کاملNotes on Polynomially Bounded Arithmetic
We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.
متن کامل