books.google.com - Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced...http://books.google.com/books/about/Ramsey_Theory_on_the_Integers.html?id=Y3r9mCOcUfoC&q=compactness+principle+ramsey+theory&utm_source=gb-gplus-shareRamsey Theory on the Integers