Closure properties of locally finite omega-languages

Locally finite ω-languages, defined via second order quantifications followed by a first order locally finite sentence, were introduced by Ressayre in [Res88]. They enjoy very nice properties and extend ω-languages accepted by finite automata or defined by monadic second order sentences. We study here closure properties of the family LOCω of locally finite omega languages. In particular we show that the class LOCω is neither closed under intersection nor under complementation, giving an answer to a question of Ressayre [Res89].