Basic notions: model theory

Abstract

Abstract In the first chapter we studied structures and some relations between them, such as isomorphism and embedding, without using a formal language. In the second chapter we introduced the formal first order language in which we can speak of structures. We also defined the fundamental semantic notions. By using such notions we were able to assert, in some cases, that a certain formula is logically valid: i.e. that it is true in all possible interpretations of the symbols contained in it. In the third chapter we proved that the notion of consequence corresponds exactly to that of deducibility. Those concepts and theorems, although very important, are not, however, the fundamental topics of Model Theory which lie precisely in the middle ground between algebra and logic.