Complete and categorical theories
María Manzano · Model Theory · 1999
Abstract This chapter is devoted essentially to the study of completeness of theories and the introduction of various methods for verifying this property, which were defined in Chapter 4. As we indicated in Chapter 5, a complete theory syntactically characterized is in itself a decision procedure; every sentence is either deducible or refutable using the theory itself as an oracle. As we will see, this means that the class of models of a complete theory is strongly connected by means of the relation of elementary equivalence.