Abstract
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.
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References
Gupta, A., & Belnap, N. (1993). The Revision Theory of Truth. New York: MIT Press.
Kripke, S. (1975). Outline of a Theory of Truth. Journal of Philosophy, 72(19), 690–716.
Martin, R., & Woodruff, P. (1975). On Representing ‘True-in-L’ in L. Philosophia, 5(3), 213– 217.
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.
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.
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.
Acknowledgements
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.
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Mackereth, S. Fixed-Point Posets in Theories of Truth. J Philos Logic 48, 189–203 (2019). https://doi.org/10.1007/s10992-018-9479-9
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DOI: https://doi.org/10.1007/s10992-018-9479-9