Wednesday, May 07, 2008

Thomas Forster

Found on T.E. Forster's page.

As a matter of fact, I'm reading Forster's nice book Logic, Induction, and Sets and was looking for a list of errata. A list that, unfortunately, I didn't find.
If you're familiar with the book, by the way, I was concerned with the second paragraph on page 59 : ok, on the third line, I guess, "continuous" should be replaced by "complete" and on the tenth line, it is the set of fn(x) for *n* in N that is of interest (I write fn(x) for the nth iteration of the function f). But on line 6-7, what's going on exactely ? Is it tacitly assumed that x is sound in the sense that x≤ f(x) [for the sup of {x, fx, etc} to be a fixed point of the continuous operator f defined on a poset assumed to be chain-complete] ? Or does it have something to do with inflationary functions, defined a few pages earlier ? The intuition on continuity is, I think, clear enough, but I'm a bit baffled by the details of the development of the discussion in this paragraph.