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I'm interested in studying mathematical logic, but I've historically been average at mathematics. I have taken the easy courses in logic at uni and I can understand prop and predicate logic in terms of soundness, validity, how to formalize arguments in them, and the sort of fallacies associate with them (the easy stuff). But I'm curious about theorems, completenes, etc.

I tried reading some "logic and structure" by van Dalen, and it is almost impossible for me to understand. (The notation isn't too bad, but I just don't follow the proofs/theorems)

Are there any intermediate texts or books for non mathematicians that explain recursion, induction, theorems etc that would be an appropriate stepping-stone towards understanding van Dalen's book, from just a basic understanding of logic? Any help would be greatly appreciated.

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    $\begingroup$ I'll suggest "Language, Proof, and Logic", which covers the basics in enough depth to reach some interesting "advanced" theorems at an easy to understand level. Enderton, or Mendelson, are sort of the next step. Understand the concepts before you try to understand the proofs. $\endgroup$ – nomen Nov 1 '19 at 23:20
  • $\begingroup$ Most definitions/propositions in the beginning involve recursion and induction. They're covered in infinitedescent.xyz (see the relevant chapters). $\endgroup$ – user524154 Nov 3 '19 at 2:20
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A good introductory logic book is a set of notes by Kueker - Kueker, Notes on Logic. (Pdf included in link)

After that, Enderton's book is good - Link to Enderton

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