I read this post on nLab and now I want to learn some order theory. What are good texts that contain the above referenced topics, and are there any that are explicitly about order theory as decategorified category theory (or categorify order theory)? I am especially interested in categorical logic so I especially want to read up on things like Boolean and Heyting algebras, and other relevant topics that I don't yet know about.
Basically I want to use order theory as a stepping stone to learning category theory, and learn some things relevant to logic as I go.