# Textbooks about non-RE languages for undergraduate students

I'd like to read up on non-recursively enumerable languages. Which textbooks should I look into to get a decent understanding about the subject?

Thank you.

(Incidentally, note that the non-r.e. elements of the arithmetical hierarchy aren't all "r.e.-hard." For example, consider any minimal $$\Delta^0_2$$ degree, that is any Turing degree $$\le_T{\bf 0'}$$ which is nonzero but not strictly above any nonzero Turing degree. There are infinitely many minimal $$\Delta^0_2$$ degrees; by the Sacks Density Theorem, they are all non-r.e. and hence by minimality don't compute any nonrecursive r.e. sets. The way in which the r.e. degrees sit inside the $$\Delta^0_2$$ degrees is actually fairly complicated.)