[3] Not counting introductory material and appendices, there are six chapters in The Higher Infinite, arranged roughly in chronological order by the history of the development of the subject.
The author writes that he chose this ordering "both because it provides the most coherent exposition of the mathematics and because it holds the key to any epistemological concerns".
[5][6] The second chapter, "Partition properties",[4] includes the partition calculus of Paul Erdős and Richard Rado, trees and Aronszajn trees, the model-theoretic study of large cardinals, and the existence of the set 0# of true formulae about indiscernibles.
[5] Reviewer Frank R. Drake views this chapter, and the proof in it by Donald A. Martin of the Borel determinacy theorem, as central for Kanamori, "a triumph for the theory he presents".
[8] Reviewer Pierre Matet writes that this book "will no doubt serve for many years to come as the main reference for large cardinals",[4] and reviewers Joel David Hamkins, Azriel Lévy and Philip Welch express similar sentiments.