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What are some good books and surveys for learning about first-order logic and monadic second-order logic?

I'm a graduate student in computer science with a focus on algorithms. For model-checking on graphs, I need to be familiar with the FO and MSO logics.

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It depends what precisely do you want to learn. A good reference is the finite model theory book by Libkin. https://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf (chapters 2 and 7).

If you want more specific references, please be more precise with your question.

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  • $\begingroup$ Thanks for the answer. First, I would like to become familiar with the definitions and theorems of FO and MSO, although not on an advanced level. Furthermore, I am interested in knowing what problems and properties in graph theory are expressed and cannot be expressed by FO and MSO. $\endgroup$
    – fva
    Jan 5, 2023 at 12:37
  • $\begingroup$ Ok, so I think that the first two chapters would be ok of Libkin's book will be ok (+ the chapter about MSO). Otherwise, you can also go through the following undergrad book: Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics) amazon.com/Mathematical-Logic-Undergraduate-Texts-Mathematics/… $\endgroup$ Jan 5, 2023 at 14:01
  • $\begingroup$ Thanks! It seems like a great book. The book "Graph Structure and Monadic Second-Orderer Logic" by Courcelle and Engelfriet was also recommended by a friend. $\endgroup$
    – fva
    Jan 6, 2023 at 16:10
  • $\begingroup$ Yes, but this is a way more advanced than the ones that I told you (say, undergrad level vs PHD student / researcher level). $\endgroup$ Jan 6, 2023 at 18:46

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