Calculating self-referential statements, I: Explicit calculations

Studia Logica 38 (1):17 - 36 (1979)
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.
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DOI 10.1007/BF00493670
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The Incompleteness Theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.
Solution of a Problem of Leon Henkin.M. H. Lob - 1955 - Journal of Symbolic Logic 20 (2):115-118.

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Sentences Implying Their Own Provability.David Guaspari - 1983 - Journal of Symbolic Logic 48 (3):777-789.

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