Induction rules in bounded arithmetic

09/27/2018

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by   Emil Jeřábek, et al.

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We study variants of Buss's theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on Π̂^b_i induction schemes, which were so far neglected in the literature. We present inclusions and conservation results between the systems (including a witnessing theorem for T^i_2 and S^i_2 of a new form), results on numbers of instances of the axioms or rules, connections to reflection principles for quantified propositional calculi, and separations between the systems.