where to begin with mathematical logic- text suggestions My name is battlefrisk and I intend to pursue a career in either operations research or artificial intelligence.  I have only taken a single class on logic, and I am considering buying a text on the subject of logic by itself as well.  I ended up desiring to study the field of mathematical logic after i found my problem solving abilities to be improving from considering the notions of well defined groups, the purpose of models, and the value of symmetries (which i define very loosely as a pattern which allows us to define one "thing" as a relatively simple transformation of another). After some time on the internet, it came to my attention that these subjects fell under a category of study called mathematical logic.  
The problem I am having in choosing a book is that I am not indoctrinated into the field, and therefore have very little to go off of when evaluating what books i should consider.  I would greatly appreciate if you kind people out there could recommend me a text for someone with my goals.  Or perhaps you could recommend that i instead improve my understanding of basic logic with a different text.  I am open to all suggestions.  
Maybe I should also mention that I am intending to study this text alongside Sipser's Introduction to the theory of Computation and some introductory text meant to help me break into the world of Operations Research.
Thank you all for your help!
 A: By far my favorite book on mathematical logic is "Computability and Logic" by Boolos, Burgess, and Jeffries, now in its fifth edition (I learned logic from the fourth ed., which is available used for cheap). I cannot recommend it highly enough.
A brief outline of the book: the first 8 chapters cover basic computability theory. This nicely complements the content of Sipser, which focuses more on the complexity side of things; there's a ton of overlap between the two, here, though. For computability, I think they're both great; Sipser's advantage is that he gives wonderful intuitive explanations of proofs.
NOTE: CaL does spend an entire chapter on abacus machines, which I found odd; you can skip it freely if you want, although it is very nicely written.
It's after chapter 8 that CaL really begins to shine. In 19 pages, chapters 9 and 10 provide the single best introduction to first-order logic that I've ever seen.
From here out the order of chapters becomes somewhat ideosyncratic: they work fine as presented, but I would read 12, 13, 14. Chapters 11 and 15-18 then present Godel's theorems.
The remaining chapters, on further topics, constitute that elusive "second course in mathematical logic" that I never had formally: a collection of serious, interesting, yet accessible advanced topics in logic, designed to whet the appetite. None of these chapters will provide mastery, but that's not the point: they are wonderfully lucid introductions to proof theory, forcing in arithmetic, combinatorics, nonstandard analysis, and second-order and modal logics, and can be read in any order.
A: While I second Noah Schweber's recommendation to read 'Computability and Logic', I also recommend this free textbook recently put together by a group of logicians aimed at providing a free and rigorous introduction to logic which goes into computability theory and meta-logic as well.
http://people.ucalgary.ca/~rzach/static/open-logic/open-logic-complete.pdf
