I was just looking for a good definition for 1-3 normal form. These do pretty well.

A relation is in 1NF if and only if all underlying domains contain atomic values only.
http://www.cs.jcu.edu.au/Subjects/cp1500/1998/Lecture_Notes/normalisation/1nf.html


A relation is in 2NF if it is in 1NF and every non-key attribute is fully dependent on each candidate key of the relation.
http://www.cs.jcu.edu.au/Subjects/cp1500/1998/Lecture_Notes/normalisation/2nf.html


A relation R is in third normal form if it is in 2NF and every non-key attribute of R is non-transitively dependent on each candidate key of R.
http://www.cs.jcu.edu.au/Subjects/cp1500/1998/Lecture_Notes/normalisation/3nf.html