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In this paper, we introduce a proof system NQGL for a Kripke complete predicate extension of the logic GL of provability. While GL is defined by K and the L¨ob formula ✷(✷p ⊃ p) ⊃ ✷p, NQGL does not have the L¨ob formula as its axiom, but has a non-compact rule, that is, a derivation rule with countably many premises, instead. We show that NQGL enjoys cut admissibility and is complete with respect...
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