TITLE: What is the best way to construct an Aronszajn Tree?
QUESTION [7 upvotes]: What is the best definition of Aronszajn tree? And, what is the best proof that it exists?
So I write the question to learn more about Aronszajn trees, any further detail is my intention to appreciate.

REPLY [3 votes]: There is also Shelah's very enjoyable construction using descending sequences of infinite subsets of $\omega$, close in spirit to Aronszajn's tree of rational sequences, and described in Judith Roitman's book here: https://www.math.ku.edu/~roitman/stb3fullWeb.pdf.