Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ

Pavelka-style (rational) Gödel logic is an extension of Gödel logic which is denoted by RGL*. In this article, due to the approximate Craig interpolation property for RGL*, the Robinson theorem and approximate Beth theorem are presented and proved. Then, the omitting types theorem for this logic is expressed and proved. At the end, as a reduction, the omitting types theorem for standard Gödel logic with Δ is studied.