Remark: In the following, the line numbers refer to the ones given in the first galley proof. Line 186: Please re-introduce twice spaces around "|" (\mid) in the intensional set descriptions in the two lines "less or equivalently specific" and "more specific or equal". Line 365, 369, 371, 374: Please re-introduce spaces around "|" (\mid) Line 500 up to 510: Your typesetting hides the structure of the text severely. Please do add some empty vertical space (blank line or paragraph) after lines 500 and 505. This means before the line (phase 2) and before the line (phase 3). There is ample space at the bottom of the page for this. Fig. 1: Please remove the note anchors 16 and 17 at their second occurrence, i.e. replace 16,17,18 in the caption with 18. It would also be nice if you could re-introduce the fullstop you deleted at the end of the caption text. If this is against your style rules, please ad some space between the "1, 2, 3" and the note mark 18. Line 599: For beauty, there should also be some extra space before the formula of Corollary 3. Note that your design is for a slanted character to start the text of the corollary. As it starts with a formula with non-slanted symbol, some space should be added according to rules of good typesetting. Example 12: It would be nice if you could remove the huge vertical spaces around the graphics a bit and get the two orphan lines from the following page to the same page as Example 12, so that the whole example is presented one on page. This will help the reader a lot to understand the difficult mathematical material. You may also add some extra vertical space before "Example 12 (Example 6 ...)". Line 963: The huge vertical space before this line and the huge vertical space after the line "Example 17 (Variation of Example 13)" do not give the reader a chance to understand that this example continues up to line 971. *** Please remove any vertical space here! *** If your vertical space is a rubber one and you cannot change this, please add a huge space before the section headline "7.3 Conflict ..." Line 1016: The huge vertical space before this line and the huge vertical space after the line "Example 19 (...)" do not give the reader a chance to understand that this example continues up to line 1024. *** Please remove any vertical space here! *** If your vertical space is a rubber one and you cannot change this, please add a huge space before the section headline "8.2 Comparing derivations" Corollary 7: The pagebreak within the lemma you introduced in your second typesetting is very ugly, in particular regarding the ample space on the bottom of the first of the pages, strongly indicating that the corollary is finished here. The user will easily miss the orphan lines. Please undo this new pagebreaking and break, if necessary, the footnote text of notes 35 and 36 to the following page, just as it was the case in your first typesetting. You can easily get more vertical space on the first of the pages by reducing the spaces around the itemization (a),(b),(c) in item 1 of definition 16, which is anyway against the rules of good typesetting: secondary enumeration should never have more space the primary ones! Line 1269: You have newly deleted some vertical space between the displayed formula and the line starting "because --- although". Please re-introduce that vertical space. Corollary 9, last line: For mathematical reasons, it is strictly necessary that you re-introduce the deleted spaces around the relation symbol (an underlined stretched capital C, with a slash trough it: \nsublseteq) This means the re-introduction of 4 spaces at least. a further space in front of the formula would be nice.