I was reading the text "Axiomatic Geometry" by John M. Lee and in the second chapter on "incidence geometry' he defined an 'interpretation' to be an assignment of a mathematical definition for each of it's primitive terms. He then defined a model as: An interpretation is said to be a model if each of the axioms is a true statement when the primitive terms are given the stated definitions.
He then goes on to give multiple examples of interpretations that are models and I have greatly enjoyed everything I have read so far. But after searching to read some more regarding interpretations and models, I came across this post and the answer goes into talking about languages and framing a theory in a language. I am assuming there is more to the definitions of interpretations and models and how an axiomatic system works. Could someone recommend some resources as to where I can learn about these things more. Or more general about axiomatic systems and where to look to learn about theories and languages? What is the subject that studies these things called? Is it all just part of mathematical logic?
