Büchi context-free languages

We define context-free grammars with Büchi acceptance condition generating languages of countable words. We establish several closure properties and decidability results for the class of Büchi context-free languages generated by these grammars. We also define context-free grammars with Müller acceptance condition and show that there is a language generated by a grammar with Müller acceptance condition which is not a Büchi context-free language.