If a rejected paper is published, is it still rejected?

There is now a new journal, Rejecta Mathematica (slogan: caveat emptor), that is dedicated to publishing articles that were rejected by other journals. The paradox of whether a rejected paper continues to belong to the set of rejected articles once it's been published in Rejecta Mathematica aside, this is not a joke.

Each article is published along with a note from the authors who say why their work is important (even if it was rejected in the traditional peer review process). The first open letter is a pretty good instance of this in action:

It is not in the literature, and does not follow in any direct or simple way from existing results. In other words, it is, as far as we know, new.

The paper that I had the hardest time getting published (this one) was also new in that it didn't follow from existing results. So, I know what these authors are talking about. Now, the paper that I had such a hard time getting accepted is widely cited.

Rejecta Mathematica figures to be a very prominent location, so these folks will probably have the last laugh.