Model vs Axiom vs Theory... difference

Question

I am not a student but I am interested in logic, I am reading a book about model theory. The problem is I guess book is not so interested in defining notions and I also couldn't understand the definitions in the internet. So I want to start from the beginning:

As I understand conjugations atomic sentences make bigger sentences and their truth value is an "assignment". A set of sentences is called a theory and if another set of sentences can "semanticly" (*isn't deriving something a syntatic task?) derive all sentences of that theory it is a model of that theory. And there is axioms that are have the same "consequence" (*what does this means?) of their theory. And can model also be axioms? What does it mean set of sentences to be "increasing"? And what does it mean a sentence to be "positive"?

I hope these questions doesn't sound ridiculous...

There are too many questions. A model is not a set of sentences, it is a structure. Instead of starting with a book on model theory, an introduction to logic seems like it would be more in order. — spaceisdarkgreen, Jan 14 '24 at 18:13
See e.g. What's a Logic? and Interpretation adn Structure and Theory. — Mauro ALLEGRANZA, Jan 15 '24 at 07:49

score 3 · Answer 1 · answered Jan 14 '24 at 19:37

This question -- or rather, very muddled bundle of questions -- strongly suggests that you are trying to run before you can walk.

Before tackling model theory, you absolutely need to get a firm grasp of first-order logic.

There are some wonderful books on FOL out there. For some suggestions to explore, to find what will work best for you, see the chapter on FOL in Beginning Mathematical Logic: A Study Guide which you can download from https://www.logicmatters.net/tyl

Model vs Axiom vs Theory... difference

1 Answers1