Gödel sorted … until the next time

Well, I’ve just this morning sent off the PDF for the next reprinting of my Gödel book: it should be available mid-August. I’ve eliminated quite a few more typos (thanks to everyone who let me know of errors in the earlier printings), made a scattered selection of small clarifications/stylistic improvements, and corrected the major errors that were still lurking even in the first corrected reprint. The biggest change is the one I mentioned a couple of posts ago, concerning Rosser’s Theorem.

Being a reprint though, I couldn’t change the “extent” of the book, the number of sheets that need printing. (Fortunately, the previous version finished on a recto page, so I had the verso to play with, and needed the extra side to correct the treatment of Rosser’s Theorems). But given a new edition, I’d like another dozen or fifteen pages. First, I’d give a nicer proof that Robinson Arithmetic can capture all p.r. functions. Second, I’d fill in all the details of the proof that Prf(m, n) is p.r. (the final stages of which are just sketched). Third, I’d fill out the proof of the derivability conditions for theories with a smidgin of induction (again, I give an arm-waving sketch). As to the second and third, I originally didn’t worry about giving sketches, as filling out the details is pretty tedious and unexciting (what you surely want to get across are the proof-ideas: and I referred masochists and completists to places where they can get the full gory story). But a number of readers have thought I should have gone the extra mile and risen to the challenge of giving full, though still maximally accessible, proofs. OK: if there’s a second edition with a slightly longer page budget I’ll have a bash … But that will have to wait a bit.