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Abstract:
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Results from model theory of mixed-valued 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 k-models (the characteristic theorem for mixed-valued predicate calculus with respect to other logics based of Post's algebras); the theorem about the connection between k-models of mixed-valued predicate calculus and models of classical predicate calculus; and the theorem of the difference between the theory of k-models of mixed-valued predicate calculus and theory of models of classical predicate calculus. By using results from the previous chapter, the theorems of mixed-valued predicate calculus (which analogous to the well-known theorems from classical predicate calculus: Craig’s interpolation lemma, Beth’s theorem about definability and the II_ε-theorem) are proved in Chapter 2. Results concerning structures of mixed-valued equivalence relations and congruence relations (which is connected with the well-known results from universal algebras about the structure of equivalence relations and congruence relations) are presented in Chapter 3. |