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17On axiom schemes for T-provably $${\Delta_{1}}$$ Δ 1 formulasArchive for Mathematical Logic 53 (3): 327-349. 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 recursion-theoretic question.
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Metaphysics and Epistemology |
Philosophy of Language |
Philosophy of Mind |
Science, Logic, and Mathematics |