The aim of this chapter is to sketch out basic model theory. We wish to summarize some key facts for people already acquainted with them, but also, at the same time, to introduce them to people unfamiliar to logic, and perhaps disliking too many logical details. Accordingly we will use a rather colloquial tone. The fundamental question to be answered is: what is Model Theory? As we will see in more detail in Section 1.2, Model Theory is -or, more precisely, was at its beginning- the study of the relationship between mathematical formulas and structures satisfying or rejecting them. But, in order to fully appreciate this matter, it is advisable for us preliminarily to recall what a structure is, and which kind of formulas we are dealing with. This section is devoted to the former concept.
KeywordsAlgebraic Variety Order Logic Relation Symbol Operation Symbol Elementary Embedding
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