The omegarule interpretation of transfinite provability logic
Abstract
In this paper we consider transfinite provability logics where for each ordinal in some recursive wellorder we have a corresponding modal provability operator. The modality [xi] will be interpreted as "provable in ACA_0 together with at most xi nested applications of the omega rule". We show how to formalize this in in second order number theory. Next we prove both soundness and completeness under this interpretation. We conclude by showing how one can lower the base theory ACA_0 to theories below RCA_0.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.5393
 Bibcode:
 2013arXiv1302.5393F
 Keywords:

 Mathematics  Logic;
 03F45;
 03F15