First-order interpolation properties are notoriously hard to determine, even for logics where propositional interpolation is more or less obvious. One of the most prominent examples is first-order G ̈odel logic. Lyndon interpolation is a strengthening of the interpolation property in the sense that propositional variables or predicate symbols are only allowed to occur positively (negatively) in the interpolant if they occur positively (negatively) on both sides of the implication. Note that Lyndon interpolation is difficult to establish for first-order logics as most proof-theoretic methods fail. In this paper we provide general derivability conditions for a first-order logic to admit Lyndon interpolation for the prenex ⊃ prenex fragment and apply the arguments to the prenex ⊃ prenex fragment of first-order Go ̈del logic.
An Algebraic Study of S5-Modal Gödel Logic
