Fixed-Point Posets in Theories of Truth

  • Stephen Mackereth


We show that any coherent complete partial order (ccpo) is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.


Truth Paradox Fixed-point theories Coherent complete partial order 


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My warmest thanks go to Anil Gupta, an excellent teacher and mentor, for his extensive comments on this manuscript. He caught my worst mistakes and clarified the argument considerably. I would also like to thank two anonymous referees for their very helpful comments.


  1. 1.
    Gupta, A., & Belnap, N. (1993). The Revision Theory of Truth. New York: MIT Press.Google Scholar
  2. 2.
    Kripke, S. (1975). Outline of a Theory of Truth. Journal of Philosophy, 72(19), 690–716.CrossRefGoogle Scholar
  3. 3.
    Martin, R., & Woodruff, P. (1975). On Representing ‘True-in-L’ in L. Philosophia, 5(3), 213– 217.CrossRefGoogle Scholar
  4. 4.
    Martínez-Fernández, J. (2007). Maximal Three-Valued Clones with the Gupta-Belnap Fixed-Point Property. Notre Dame Journal of Formal Logic, 48(4), 449–472.CrossRefGoogle Scholar
  5. 5.
    Martínez-Fernández, J. (2014). Remarks on the Gupta-Belnap fixed-point property for k-valued clones. Journal of Applied Non-Classical Logics, 24(1-2), 118–131.CrossRefGoogle Scholar
  6. 6.
    Visser, A. (2004). Semantics and the Liar Paradox. In Gabbay, D., & Guethner, F. (Eds.) Handbook of Philosophical Logic. 2nd edn., (Vol. 11 pp. 149–240): Springer.Google Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.University of PittsburghPittsburghUSA

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