Arithmetic Interpretations of PRL
PRL has, as we have seen, moderately interesting syntactic properties and a similarly interesting model theory. Moreover, as I have intimated on occasion, it has much to say about the syntax of arithmetic: The de Jongh-Sambin Theorem, for example, applies directly to self-referential sentences of PRA— those arising from modal contexts have explicit, non-self-referential explications. The relation between PRL and PRA, however, is deeper than this. PRL is the modal logic of provability within PRA and we now have the tools to prove this.
KeywordsModal Logic Kripke Model Completeness Theorem Boolean Combination Modal Context
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