Lukasiewicz MV-algebra; model theory in fuzzy logic with evaluated syntax.

This paper presents a model theory respective theory of omissions of types, where the basic mathematical theory is fuzzy logic in narrow sense with evaluated syntax. For this work we assume fuzzy logic with evaluated syntax which is based on \L ukasiewicz MV-algebra of truth values (see \cite {Novak-Mockor-Perfilieva}), but this theory can be constructed for other fuzzy logic with evaluated syntax for example fuzzy logic with evaluated syntax extended by product where the corresponding structure of truth values is \L ukasiewicz MV-algebra extended by product. For further discussion of this logic (see \cite {Murinova-Landecka},\cite{Murinova}) where was shown that this logic is complete and the model theory was studied (substructure, elementary substructure, chain of models). In this paper we introduce the basic definitions and results of this theory where we suppose special set of evaluated formulas which will be formulated later.

This paper presents a model theory respective theory of omissions of types, where the basic mathematical theory is fuzzy logic in narrow sense with evaluated syntax. For this work we assume fuzzy logic with evaluated syntax which is based on \L ukasiewicz MV-algebra of truth values (see \cite {Novak-Mockor-Perfilieva}), but this theory can be constructed for other fuzzy logic with evaluated syntax for example fuzzy logic with evaluated syntax extended by product where the corresponding structure of truth values is \L ukasiewicz MV-algebra extended by product. For further discussion of this logic (see \cite {Murinova-Landecka},\cite{Murinova}) where was shown that this logic is complete and the model theory was studied (substructure, elementary substructure, chain of models). In this paper we introduce the basic definitions and results of this theory where we suppose special set of evaluated formulas which will be formulated later.