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.