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I want to read model theory and would like suggestion of a book which is a good place for a beginner with no background of logic.

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    $\begingroup$ David Marker has a nice book on model theory which I plan to read some time in my life. I think you need to learn some mathematical logic first (syntax of FOL, naive set theory, formal proofs, soundness theorem , compactness theorem , Godels completeness and incompleteness theorem, a little comparability theory) before jumping into model theory $\endgroup$
    – Amr
    Oct 27, 2021 at 20:05
  • $\begingroup$ Do you have a solid background in mathematics (e.g. good courses on analysis, algebra, topology, etc.)? Because I don't see how you can tackle model theory without some good knowledge of either logic or mathematics (preferably both)... $\endgroup$
    – Nagase
    Oct 27, 2021 at 20:28
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    $\begingroup$ @Nagase Yes, I have knowledge of the former. I'm a second year master student with a focus on functional analysis. I have never taken any course on logic. $\endgroup$ Oct 27, 2021 at 20:29
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    $\begingroup$ akruckman.faculty.wesleyan.edu/files/2019/07/Lecture-Notes.pdf $\endgroup$ Oct 27, 2021 at 20:38

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Since you indicated that you have a good background in math, here are a couple of books for learning model theory.

The first is An Invitation to Model Theory, by Jonathan Kirby. It is a bit terse, but it provides all the necessary definitions and does not presuppose that you are already familiar with logic---the first three chapters provide all the necessary background, and the standard theorems (Compactness, Löwenheim-Skolem) are all proved in the text. It also has a more modern feel than most textbooks in the area, I think, since it focus from the beginning on definability issues, which are central to current model theory.

The second, much more advanced, is Bruno Poizat's A Course in Model Theory. In my opinion, it is one of the best texts on the topic, even if it is highly idiosyncratic---e.g. instead of starting by defining formulas, etc., Poizat begins with the notion of a local isomorphism, only later relating this to a language. Still, the chapters on compactness and the space of types are really good at understanding what is going on with those theorems, and the chapter on arithmetic contains one of the best discussions of Gödel's incompleteness theorems. Indeed, even if you read the book only up to that chapter, you'd already have a really good introduction to the subject (though not one that would bring you up to date with current research).

Somewhat easier than Poizat is Rothmaler's Introduction to Model Theory, which also does not assume any background in logic. Finally, if you really like doing exercises and want to learn the back-and-forth technique explored by Poizat in a more elementary setting, Kees Doets Basic Model Theory is really nice.

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I highly recommend the new book by Jonathan Kirby: https://www.cambridge.org/highereducation/books/an-invitation-to-model-theory/CC61059C533D4799D77E1BECEBC21C47#overview

It is (as far as I am aware) the first undergraduate-level book on model theory, and it certainly assumes no background on logic. Individual chapters are short and easily digestible, and the exercises are enlightening.

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