Arithmetic Interpretations of PRL

  • C. Smoryński
Part of the Universitext book series (UTX)


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.


Modal Logic Kripke Model Completeness Theorem Boolean Combination Modal Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • C. Smoryński
    • 1
  1. 1.Department of Mathematics and Computer ScienceSan Jose State UniversitySan JoseUSA

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