Abstract
Locally finite ω-languages, defined via second-order quantifications followed by a first-order locally finite sentence, were introduced by Ressayre (J. Symbolic Logic 53(4) (1988) 1009–1026). 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 LOC ω of locally finite omega languages. In particular, we show that the class LOC ω is neither closed under intersection nor under complementation, giving an answer to a question of Ressayre (Question posed during a Working Group on Automata and Logic at University Paris 7, 1989).
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