1NF is defined as eliminating nested relations. I assume "[ cryptography, databases]" in the example represent a nested relation.

1NF is not defined in terms of what you want to do with the the data, it is defined in terms of domains, i.e data types. If a column allows nested tables, it violates 1NF.

"Atomic" in the context of 1NF means atomic wrt. the relational algebra.

Eg. if we have:

   Student: Bob, classes: [ cryptography, databases]
   Student: Alice, classes: [] 

Is it possible to select from this all students which has cryptography as a class, using the standard relational operators (project, filter, join)?

I think we're mostly in agreement!

You're right, it's not possible to select from this all students which has cryptography as a class. No more than if we did concat('cryptography', ',', 'databases').