Right. I really must get on with other work (in particular the task of writing exercises for the Gödel book awaits). But, as an exercise in constructive procrastination I’ve just uploaded the February 2013 version of the Teach Yourself Logic Guide.
Chapter 1 on The Basics is in a reasonably stable state, and I’ve only tinkered with that in small ways since the last version as uploaded back in November. I’ve added another section to Chapter 3, ‘Exploring Further’. But the big change is that I’ve started work on the new Chapter looking at some of the Big Survey Books on mathematical logic. There’s quite a long list to work through — I must be mad to have taken this task on myself! — so don’t hold your breath waiting for the entry on your favourite book. Still, between you and me, it has been enjoyable to dive in, blow the dust off some old acquaintances, and remind myself what they get up to. So I do plan to continue adding entries sporadically.
I’ve added to the Guide the entries on the classic texts by Kleene, Mendelson and Shoenfield of which I posted drafts here. As a bonus I’ve also just added an additional entry on Joel Robbin’s 1969 book Mathematical Logic: A First Course. Yes, yes, that doesn’t really come next in chronological order and it isn’t exactly a Big Book either (the main text is just 170 pages). But it does cover an interesting amount in a short space. And having been a bit grouchy about Mendelson and very grouchy about Shoenfield, I’m inclined to be rather warm about this. My summary verdict is
A different route through this material [first- and second-order logic, primitive recursive arithmetic, PA2, Gödel's theorem], Robbin’s book is accessibly written and still worth reading. Look especially at Ch. 3 for the unusually detailed story about how to build a language with a function expression for every p.r. function, and at the last chapter for how to work in PA2.
For more details, see the Guide!