# Extensions of $\omega$-Regular Languages.

@article{Bojanczyk2020ExtensionsO, title={Extensions of \$\omega\$-Regular Languages.}, author={Mikolaj Bojanczyk and Edon Kelmendi and Rafal Stefanski and Georg Zetzsche}, journal={arXiv: Formal Languages and Automata Theory}, year={2020} }

We consider extensions of monadic second order logic over $\omega$-words, which are obtained by adding one language that is not $\omega$-regular. We show that if the added language $L$ has a neutral letter, then the resulting logic is necessarily undecidable. A corollary is that the $\omega$-regular languages are the only decidable Boolean-closed full trio over $\omega$-words.

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