[Proof Complexity] preprint

Emil Jerabek jerabek at math.cas.cz
Thu Sep 27 20:56:47 CEST 2018

Dear colleagues,

A new preprint "Induction rules in bounded arithmetic" is available on
my web page (http://math.cas.cz/~jerabek/index.html). Suggestions,
corrections, and comments are welcome.

Best regards,
Emil Jerabek

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 \Pi^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.

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