Arithmetic Interpretations of PRL

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

Abstract

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.

Keywords

Timothy 

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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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