TITLE: The order type of the rationals.
QUESTION [8 upvotes]: Herewith another mind-numbingly naive question from a reader of philosophy.
My question concerns the order type of the rational numbers.  
Omega squared seems a natural first choice, but obviously this does not look anything like the natural ordering of the rationals.
Is it known where the order type of Q occurs in the hierarchy of ordinal numbers?  Is there a known ordinal-arithmetic expression describing it a function of omega?  
Finally, I really must buy a textbook on the subject of Set Theory.  Wiki is a fantastic resource and the maths pages are of exceptionally high quality, but I don't want to get into bed at night with my laptop.  Is there a standard, undergraduate text that could be recommended.

REPLY [4 votes]: E. Kampke's book on set theory, which I think has a Dover edition, has some material on the order type of the rationals.  It's not found among the ordinals because it's not well-ordered.  However, there's a proof, which I seem to recall goes back to Cantor, proving that any two countable linearly ordered sets without endpoints that are densely ordered (i.e. between any two points there's another) are order-isomorphic.