TITLE: What are the prerequisites for studying mathematical logic?
QUESTION [16 upvotes]: I am looking to study mathematical logic, however, I find that introductory books are very daunting, which kind of disheartens me. You see, slowly but surely, I started to realize that the maths which I have learned did not just pop out of thin air, but is a collection of systems, which must of been developed via some other system, i.e, maths did not develop itself.
So I began to look into the origins of mathematics, and read that it was developed via a type of logic, which exists sort of by 'default', via a set of axioms, and then of course I looked up the definition of axioms. 
So given that I'd be studying a type of logic whose origins are self evident axioms, naturally I believed there would be no prerequisites. However, in looking up mathematical logic, I have come across things such as Boolean algebra, sets, first order logic, some other type of logic, called 'traditional logic', as well as references to a sort of calculus, though not in a mathematical sense, I think.
So all in all, I am trying to develop a type of mental spider web, and I am trying to find out the strands which lye at the absolute bounds so that I may learn this mystique logic. Though I have no idea where to start.
Side note: This is the book I have started reading: http://www.dainf.cefetpr.br/~kaestner/Logica/MaterialAdicional/announceRautemberg.pdf
Credit goes to Wolfgang Rautenberg.

REPLY [5 votes]: This is an old question, butlet me plug my favorite logic textbook: "Computability and Logic" by Boolos, Burgess, and Jeffrey. As the name implies, it has a strong computability-theoretic focus which you may not be interested in; however, it also has a self-contained treatment of first-order logic logic (chapters 9-10 and 12-14) which I found the clearest by far of the books I had access to when I was first learning this stuff. Its presentation of Godel's theorems (chapters 11 and 15-18, building on chapters 1-4 and 6-7) is also excellent, in my opinion. (And besides, computability theory is really cool.)
It ends with a collection of further topics; some of this material is usually only covered in more advanced and specialized courses, but it's actually quite accessible, so it's nice to have it in one place in a more introductory text. I'm not sure I would have chosen those exact topics to include rather than others, but it's certainly a reasonable selection.