The liar paradox and fuzzy logic

Journal of Symbolic Logic 65 (1):339-346 (2000)
Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}(\bar{\varphi})$ for all sentences φ? This problem is investigated in the frame of Lukasiewicz infinitely valued logic
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DOI 10.2307/2586541
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Hannes Leitgeb (2008). On the Probabilistic Convention T. Review of Symbolic Logic 1 (2):218-224.

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