A Lindström theorem for modal logic

A modal analogue of Lindstrr om's characterization of rst-order logic is proved. Basic modal logics are characterized as the only modal logics that have a notion of nite rank, or, equivalently, as the strongest modal logic whose formulas are preserved under ultra-products over !. Also, basic modal logic is the strongest classical logic whose formulas are preserved under bisimulations and ultra-products over !.