levels of expertise

setting rules:

level who can set + requirements
<=‘beginner’ oneself
‘apprentice’ someone else >= ‘intermediate’
‘intermediate’ someone else >= ‘advanced’
‘advanced’ someone else >= ‘master’
‘accomplished’ oneself = ‘advanced’ + someone else >= ‘master’
‘master’ one’s apprentice =‘accomplished’ + someone else >= ‘grandmaster’
‘grandmaster’ one’s apprentice >= ‘master’ + other >= ‘grandmaster’
‘great grandmaster’ similar to ‘grandmaster’

I know that without additional logic one can’t graduate to ‘master’ and ‘grandmaster’, extra logic for existing ‘master’(s) required. For example when 2 or 3 people from one level can act as one person from level above.