
17On axiom schemes for Tprovably $${\Delta_{1}}$$ Δ 1 formulasArchive for Mathematical Logic 53 (3): 327349. 2014.This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are $${\Delta_1}$$ provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether $${I\Delta_0 + \neg \mathit{exp}}$$ implies $${B\Sigma_1}$$ to a purely recursiontheoretic question.
Areas of Specialization
Metaphysics and Epistemology 
Philosophy of Language 
Philosophy of Mind 
Science, Logic, and Mathematics 