## Peter Hinman A very good example of someone smack in the middle of ω is Peter Hinman. His book was written over 20 years, and it's clear in its intent to express standard foundations of mathematics in all its forms except proof theory which is fine because most of us don't know much proof theory anyway. But he succeeds in his goal: Cover as much as possible of 20th century logic as it appears from the viewpoint of the early 21st. He covers about as much of the standard foundations as one could hope for, with a notation designed to painstakingly distinguish the metalanguage from the formal language. And as jarring as that notation might feel at first glance, it's essential to have a book like this in the field because nobody else in the field does that as consistently as Hinman so it's a clarifying example of a fundamentally important distinction that most of the other skilled authors gloss over. I think Hinman is a better example of a Λω than anyone I know. ## Thomas Jech Jech, on the other hand, is not a Λω or even really a full ω, he's an ω in the sense of set theory with a measurable touch of Ω. ## The Big Omegas Kanamori and Kunen are pure Ω, though Kunen's FOM book has a sizable amount of ω too while presenting a view of "foundations" with almost no Λ.