TITLE: Canonical functions in set theory and their applications
QUESTION [9 upvotes]: Given regular cardinal $\kappa>\omega,$ we can define the canonical functions $f_\alpha: \kappa\to \kappa,$ for $\alpha<\kappa^+.$ 
Some of their properties are presented in Chapter 22 of the book "Problems and Theorems in Classical Set Theory" by Péter Komjáth and Vilmos Totik.
(A) I am looking for more references and additional properties of these functions.
(B) I also want to know what are the main applications of these functions, and how they can be used in proving theorems (in particular $ZFC$ results).

REPLY [5 votes]: In belated partial response to (A), canonical functions are certainly already defined in the Jech-Shelah paper: A note on canonical functions, where reference is made to the work F. Galvin and A. Hajnal, Inequalities for cardinal powers, Annals of Math. 101 (1975), 491-498. The name "canonical" appears to derive from the property that if they exist, they are unique up to equivalence modulo a club. Below $\aleph_2$, they always exist; at or above, they may or may not.