Interestingly, there is a bit of dispute over the term "cathedral" due to some Protestant denominations building large churches and calling them cathedrals. A cathedral, as this article points out, is only a cahedral if a bishop is present.
For example, take the Crystal Cathedral in Garden Grove, Calif. It wasn't a cathedral in the proper sense in that there was no bishop -- a position found only in Catholic (Roman or Orthodox), Anglican and some Lutheran and Methodist churches. However, it will be a cathedral in the proper sense when it reopens in 2016 as Christ Cathedral as the ownership of the building has changed hands from a Reformed Church of America facility to the Roman Catholic Church.
In other words, the building may be impressive but no bishop means its not a cathederal.