User blog comment:Denis Maksudov/Slowly growing ordinal function and FS up to BHO./@comment-28606698-20170402064919/@comment-1605058-20170402113139

You are right that this should have been stated in terms of cofinality. What you call "uncountable" really should be "with cofinality \(\Omega\)" and what you call "limit" should be "with cofinality \(\omega\)". Ordinals like \(\Omega+\omega\) or even \(\Omega+1\) are (under standard meaning of these terms) uncountable, and \(\Omega,\Omega^2+\Omega\) are limit ordinals.