Thanks. This looks like some interesting reading material. I have included an untitled chapter that is a mixed bag of philosophical issues etc. in my AI lecture (as a follow up to the chapters on propositional calculus and first order logic) and am always on the lookout for simpler ways to explain things.
Currently it's Kantor->Gödel(+ some historical background on Hilbert program/Principia etc.)->Turing(halting problem as it relates to the incompleteness theorems)->Cohen on the math front (+Chaitin numbers and some other random ideas)
The author, Peter Smith. has a wonderful blog on topics in Logic at [0]. He is planning on releasing a series of posts that will become GWT2, but his most recent post [1] explain why this has been delayed. He is also the author of a textbook on Introduction to Gödel’s Theorems [2], of which GWT is a compression. A second edition of Introduction to Gödel’s Theorems was recently released. He also has a fantastic resource, Teach Yourself Logic Guide [3], which is a collection of pointers of resources to teach yourself properly mathematical logic. He has plenty of other helpful resources that I won't directly point out, except to look under the heading Explore all this site on the front of his blog, along with the individual posts of course.
[0] http://www.logicmatters.net/blogfront/
[1] http://www.logicmatters.net/2013/09/gwt-and-tyl-on-hold/
[2] http://www.logicmatters.net/igt/
[3] http://www.logicmatters.net/2013/08/tyl-17-the-teach-yoursel...