In Section 2.1.1 the word `complement’ must occasionally be added in front of . E has pointed this already above.

– Last sentence of fourth paragraph of Section 2.1.1 `Thus is a subset of the complement of .’

– First sentence of sixth paragraph Section 2.1.1 `… and partitioning the complement of into maximal…’

– The last paragraph (of the page and/or the section) needs a little more care. Near the middle `… we can throw points and partition the rest of the complement of into long arithmetic progressions.’ On the next line though one must consider and not its complement! So the existing `Since has density at least…’ is OK.

I may have missed an instance or two.

2. The two $\delta/4$s.

This is a comment rather than a correction that I am taking the liberty to make. In the last paragraph of Section 2.1.1 the density of both and of its complement are bounded from bellow by $\delta /4$.

The reasoning behind these identical lower bounds is rather different: contains part of a translate of $\latex A_L$ while the complement of contains .

To prevent a careless reader (like myself), who may not initially pay attention to the word `complement’, from assuming that the two $\delta/4$s arise for identical reasons it may be better to turn one of them into, say, $\delta/3$.

In fact adding a very brief explanation why the density of in is at least a constant multiple of would fit in well with what is mentioned later in the discussion why making the strategy work for longer progressions is difficult (first paragraph of p.6).

3. As mentioned above in the middle of the last paragraph of Section 2.1.1 the appearing should be .

4. Near the end of the last paragraph of Section 2.1.1: `… and has density roughly in …’

5. Middle of first paragraph on p.5: `… for some positive integer …’ rather than .

6. Last sentence of first paragraph on p.5: `Since , …’

7. p.5 a formal definition of the dimension of a Hilbert cube is not given, though everyone can guess what it is.

8. First paragraph of p.10: …such that the pair is not …` i.e. turning a capital `I’ to an an `i’.

9. p.17 line -9 or so: a couple of parentheses are misplaced in the lower bound for . The } in the end should also be removed. The correct form is .

]]>on p.16, in the first line of the proof of Lemma 4, you probably don’t need to square on the left hand side.

By the way, in connection with it might be interesting to mention not only Kim’s result, but also the recently obtained lower bound of , improving the constant in the denominator from about 162 to just 4. Similarly one could think about mentioning that the constant in Corollary 1 can be taken to be .

]]>Last line of p.32: “diffierence”. (You might want to fire your spell-checker!)

p.30 line -3: According to MathSciNet, “S\’arkozy” should be “S\’ark\”ozy”.

and really scraping the barrel:

in the first 3 items of the bibliography, Koml\’os is only “J” rather than “J.”

]]>I suggest you read my views more carefully.

]]>“Emphatically not. I don’t, however, know anything about the details of their arrangement with the Norwegian Academy of Sciences.”

Considering your view on “open access”, which is tantamount to a view that authors should pay to have their work published, why did you not decline?

]]>Then, in the fifth paragraph, the parameter k in R(3,k) becomes n.

]]>Ah — I had forgotten what I called the talk. Thanks for pointing that out.

]]>there might be some confusion in future when referencing it. ]]>

The explanation for that is that I was unsure what the right convention was. My vague intention was not to put dots at the end of section titles but to put them there for subsections and below. Anyhow, I’ll get that sorted out — now that I’ve read your comment and found your advice backed up after a quick Google search, I’ll remove all the full stops.

]]>One of the greatest… ]]>

“Did Springer charge you page charges to write an article for this volume”

Emphatically not. I don’t, however, know anything about the details of their arrangement with the Norwegian Academy of Sciences. **Update March 13th:** I now know for certain that the Norwegian Academy of Sciences did not pay Springer to publish the book. Rather, they chose Springer from a number of competing publishers, and part of the reason for their choice was precisely the deal that they could post the entire book on their website.

I am glad Springer does wonderful things for the Mathematics community, but I would like to ask you a question related to your excitement about open access. if Did Springer charge you page charges to write an article for this volume, and were they comparable to the costs incurred by authors of unfunded research articles published in open-access journals?

]]>