I've skimmed https://en.wikipedia.org/wiki/Database_normalization before and I'm trying to reconcile your clear explanation with what is there.

  > Informally, a relational database relation is often described as "normalized" if it meets third normal form.

So then I look at https://en.wikipedia.org/wiki/Third_normal_form , which has this fun:

  > An approximation of Codd's definition of 3NF, paralleling the traditional pledge to give true evidence in a court of law, was given by Bill Kent: "[every] non-key [attribute] must provide a fact about the key, the whole key, and nothing but the key".[7] A common variation supplements this definition with the oath "so help me Codd".

I don't see how that relates to your normalization. It's possible the simple case of booleans was just for illustration, but if not, then it suggests to me that there should never be any boolean column in the normalized schema, since you can have an additional table containing the keys corresponding to e.g. `true` values.

Could anyone clarify?