Many thanks to all those who have told me about typos and worse, and suggested needed corrections. The latest printings are less error-prone than the earlier versions as a result, but sadly there are still some to be found, though only a handful of substantial ones. So if you are using the fourth printing, 2009, or later printings
- Check this page to see the known issues about this revised version.
If you are using earlier printings, things get a bit more complicated – but of course, the easiest thing is to ensure that you and/or your library do have the current printing (and jolly cheap it is too!). Anyway …
If you are using the corrected second printing, 2008:
- Consult the list of corrections between the second and fourth printing;
- Also look at for the needed corrected pages on Rosser’s theorems;
- Then look at the further corrections for the current fourth printing.
If you are still using the original 2007 printing (or, improbably, that rogue third printing):
- Consult the list of corrections between the first and the fourth printing;
- Also look at for the needed corrected pages on Rosser’s theorem;
- Then look at the further corrections for the current fourth printing.
IGT, p. 134, R12, Proof: (sorry for the lack of symbols!)
Var(n) = def (there is an x < = n) (n = 2 raised to 2x)
According to this definition, it seems to me, "Var(1)" is true: 0 is < = 1, and 1 = 2 raised to 2 times o.
But 1 is not the g.n. of a variable!
So perhaps one should write:
Var(n) = def (there is an x < = n) (n = 2 raised to 2x AND x is not 0).
If I am right, this is a correction, if I am wrong, it is a question (why is your definition correct?)
Many thanks for your wonderful book!
I look forward to the second edition (…and as I have written a few weeks ago, I would like to know how to prove that Sent(n) and Axiom(n) are p.r: the missing links to fully satisfy an enthusiast completist)