Abstract:

Results from model theory of mixedvalued predicate calculus are presented, by using results of the model theory of classical predicate calculus. The thesis consists of four chapters. The basic notions, definitions and properties are given in the introductory chapter. The main theorems, which are proved in Chapter 1, are the following: the weak separable theorem for kmodels (the characteristic theorem for mixedvalued predicate calculus with respect to other logics based of Post's algebras); the theorem about the connection between kmodels of mixedvalued predicate calculus and models of classical predicate calculus; and the theorem of the difference between the theory of kmodels of mixedvalued predicate calculus and theory of models of classical predicate calculus. By using results from the previous chapter, the theorems of mixedvalued predicate calculus (which analogous to the wellknown theorems from classical predicate calculus: Craig’s interpolation lemma, Beth’s theorem about definability and the II_εtheorem) are proved in Chapter 2. Results concerning structures of mixedvalued equivalence relations and congruence relations (which is connected with the wellknown results from universal algebras about the structure of equivalence relations and congruence relations) are presented in Chapter 3. 