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Undecidability of a weak version of MSO+U

We prove the undecidability of MSO on $\omega$-words extended with the second-order predicate $U_1(X)$ which says that the distance between consecutive positions in a set $X \subseteq \mathbb{N}$ is unbounded. This is achieved by showing that adding $U_1$ to MSO gives a logic with the same&nbsp;[&hellip;]