All intermediate logics with extra axioms in one variable, except eight, are not strongly omega-complete

In [8] it is proved that all the immediate logics axiomatizable by formulas in one variable. except four of them, are not strongly complete. We consid erably improve this result by showing that all the intermediate logics axio matizable by formulas in one variable, except eight of them, are not strong ly omega -complete. Thus. a definitive classification of such logics with r espect to the notions of canonicity, strong completeness, omega -canonicity and strong omega -completeness is given.