3 research outputs found
Admissible closures of polynomial time computable arithmetic
We propose two admissible closures and of Ferreira's system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) is conservative over PTCA with respect to sentences, and (ii) is conservative over full bounded arithmetic PHCA for sentences. This yields that (i) the definable functions of are the polytime functions, and (ii) the definable functions of are the functions in the polynomial time hierarch
Elementary explicit types and polynomial time operations
This paper studies systems of explicit mathematics as introduced by Feferman [9, 11]. In particular, we propose weak explicit type systems with a restricted form of elementary comprehension whose provably terminating operations coincide with the functions on binary words that are computable in polynomial time. The systems considered are natural extensions of the first-order applicative theories introduced i