Recently, I am learning the Kunen's set theory. Now I will reach the second part of the book, i.e., the important Martin Axiom is introduced here. I found it is a little complex and difficult for a beginner set theorist. I havn't any intuition for it. Could someone give me some simple examples? It's better to introduce some materials on Martin Axiom, such as video, ppt and so on. Thanks ahead:)
If you really want to understand Martin's Axiom, read the book by Fremlin ("Consequences of Martin's Axiom"), which discusses the different variants, etc., but does not deal with proving it's consistency, using iterated forcing. IMHO, seeing the axiom used on actual problems from topology, measure theory etc. greatly enhances your understanding of it.
A more accessible approach to this, also not doing the iterated forcing, but more towards building some intuition for it, can be found in "Discovering Modern Set Theory" (part 2) by Just and Weese (the AMS bookstore sells it), especially the chapter "From the Rasiowa-Sikorski lemma to Martin's Axiom".