On the Provability Logic of HA
Abstract
We axiomatize the provability logic of and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the introduction of a new type of semantics, termed provability models, for modal logics extending iGL. This semantics combines elements of standard Kripke semantics with provability in propositional modal logics.
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