The Craig Interpolation Property in First-order Gödel Logic

Abstract

In this article, a model-theoretic approach is proposed to prove that the first-order Gödel logic, $\mathbf{G}$, as well as its extension ${\mathbf{G}}^{\Delta }$ associated with first-order relational languages enjoy the Craig interpolation property. These results partially provide an affirmative answer to a question posed in [Aguilera, Baaz, 2017, Ten problems in Gödel logic].