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
The provably terminating operations of the subsystem PETJ of explicit mathematics
In Spescha and Strahm [15], a system PET of explicit mathematics in the style of Feferman [7, 8] is introduced, and in Spescha and Strahm [16] the addition of the join principle to PET is studied. Changing to intuitionistic logic, it could be shown that the provably terminating operations of PETJ i are the polytime functions on binary words. However, although strongly conjectured, it remained open whether the same holds true for the corresponding theory PETJ with classical logic. This note supplements a proof of this conjecture. Keywords: Explicit mathematics, polytime functions, non-standard model