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.