Model Theory in Many-Valued Predicate Logics∗

predicate logics. Formal theory of fuzzy logic is now a mature theory whose fun-damental problems seem already to be solved. Now, it is time to continue its development further and to study possibilities for gener-alization of all the classical results that may be useful for its main goal — to develop a mathematical theory providing tools for modelling of the vagueness phenomenon. Among such results no doubts belongs the model theory of classical logic which can be found in [6, 1]. There are several systems of fuzzy logic in narrow sense. Most of them have traditional syntax but with many-valued special interpreta-tion. We interested in two many-valued fuzzy logics namely predicate fuzzy logic with evaluated syntax (EvÃL from now one) which was intro-duced by Novák in [11] where also its model theory has been founded and basic predicate fuzzy logic (BL ∀ from now one) which was pub-lished by Hájek in [3]. It is specific for EvÃL that the set of truth values must be the ÃLukasiewicz MV-algebra whose support set is the inter-val of reals [0, 1] and BL-chains for BL∀. Model theory in BL ∀ has been initiated in [3]. Later this theory has been further elaborated by Cintula and Hájek in [4]. In [9] was introduced the omitting types theory for BL ∀ and EvÃL that contains the omitting types theorems which give the way how ∗This paper is supported by Grant MSM6198898701 1 to construct the models when the situations are too complicate to be expressed by one formula but can be expressed using a set of formulas. In the end of this paper we must say that in the model theory of predicate fuzzy logics are a lot of open problems for example the construction of non-standard models. But there is a question if it is possible to construct these models using omitting types theory