NO!!
You dive according to your certification, training and experience, AND THE EQUIPMENT YOU ARE CARRYING WITH YOU. I am certified to dive solo (whatever that means) but if I don't have the necessary redundant equipment with me (the most important of course being an alternate air supply) then I MUST NOT dive alone.
This is not just semantics, playing with words, nor is it a detail that "of course is understood". It is fundamental. I have seen too many people diving completely alone (not just technically without a buddy, but out of sight of anyone else) with eg. a single tank at great depth. I challenged one of them back on the boat - she replied rather arrogantly that she was a PADI instructor and of course was qualified to dive by herself, and who was I to question her? I didn't reply - no point. I wonder if she's still alive?