Studia Logica

, Volume 38, Issue 1, pp 17–36

Calculating self-referential statements, I: Explicit calculations

  • Craig Smorynski

DOI: 10.1007/BF00493670

Cite this article as:
Smorynski, C. Stud Logica (1979) 38: 17. doi:10.1007/BF00493670


The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation in the modal logic. We survey techniques for the efficient calculation of such fixed-points.

Copyright information

© Polish Academy of Sciences 1979

Authors and Affiliations

  • Craig Smorynski
    • 1
  1. 1.Westmont

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