Rational Pavelka predicate logic is a conservative extension of łukasiewicz predicate logic

Journal of Symbolic Logic 65 (2):669-682 (2000)
Abstract
Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963
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    Christopher J. Eagle (2014). Omitting Types for Infinitary -Valued Logic. Annals of Pure and Applied Logic 165 (3):913-932.
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