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I am looking for resources for an introduction to formal logic, with the aim of being able to understand a proof of Gödel's completeness theorem for 1st order logic. I have some background in set theory and algebra (mathematics undergraduate degree), but I never took courses in formal logic or foundations of mathematics.

A lot of the introduction books and web resources I find are oriented toward someone with a more philosophical less mathematical background, or are very detailed in outlining the problems encountered in trying to make logical interpretations of natural language sentences. I would be particularly interested if anyone had any recommendations of online resources (videos, or websites), as well as texts that specifically describe first order logic in a mathematically concrete and concise way.

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    Enderton's text "A Mathematical Introduction to Logic" would be a good introduction.
    – nwr
    Oct 18, 2016 at 2:40
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    I can recommend Mendelson's Introduction to Mathematical Logic - now in its 6th edition, it has been a standard textbook for a long time.
    – Bumble
    Oct 18, 2016 at 9:24

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Ebbinghaus, Flum, &Thomas is perfect for somebody like you. http://www.springer.com/us/book/9780387942582

the goal is just what you want: Gödel's Completeness theorem. the presentation is superb.

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  • fwiw, it is mathematically oriented, but I (not a real mathematician) found it quite readable.
    – user20153
    Oct 18, 2016 at 21:33
  • Perfect. Thank you! That is just the kind of book I am looking for.
    – postylem
    Oct 18, 2016 at 22:45
  • feel free to mark my answer ;)
    – user20153
    Oct 18, 2016 at 22:46
  • ah right, done!
    – postylem
    Oct 18, 2016 at 23:02

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