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As reported earlier, I have finished writing all material for the book
BOOLEAN RELATION THEORY AND INCOMPLETENESS
except for the Introduction (see below).
I have finished proofreading and perfecting the first four Chapters of the six Chapters total. Small errors only were detected, and corrected. There has been substantial improvement in exposition. This is important since the book has very detailed very complete proofs. As many of you know, I deliberately use a great deal of English (within limits) to make proofs easy to read and digest.
My brain almost fried perfecting Chapter 3. There I analyze 6561 ordered pairs of Boolean relations in three set variables with two functions, under 5 attributes, and derive a compactness result by pure inspection. The compactness result is provable with Mahlo cardinals of finite order, but not in ZFC. There are a total of 32,805 determinations made in that Chapter. Of course, the symmetry and some general theory save me from disappearing off the face of the earth carrying this out in Chapter 3. But the remarkable thing is that all 32,805 determinations are carried out in RCA0 except for exactly 12. Chapters 4,5 are devoted to showing that these 12 exceptions are each provably equivalent to the 1-consistency of Mahlo cardinals of finite order.
Assuming that the meticulous line by line proofreading continues to reveal at most minor problems, I expect to be done before Christmas - all but the Introduction (see below). I will put the book on my website at that time.
The Introduction will have no proofs, but will include a complete survey of my entire work on the incompleteness phenomena. Hence the expanded title. I am thinking of this Intro being essentially an adaptation of earlier survey papers, published and unpublished, including the rather extensive unpublished Rademacher Lectures, already on the web - but updated to describe recent work on lengths of proofs, Pi01 sentences, and Prefix Theory, and miscellaneous developments.
Any comments or suggestions welcome.
Harvey Friedman