Topoi, Heyting algebra and Lawvevre's CAT book

Hello, This is a followup question to my other question about topoi and intuistionistic logic. On page 350, Lawvere is talking about logical operations (in a Heyting algebra I think??). In particular I having trouble understanding the narrative on the implication operation "=>" in the sense 1) I don't understand what <alpha, beta>. (e.g. is alpha meant to be an element: alpha:1->omega?) 2) also what alpha "subset" beta is! Please help me. Thanks and regards, Bill Halchin