Abstract
This paper is about MSO+U, an extension of monadic second-order logic, which has a quantifier that can express that a property of sets is true for arbitrarily large sets. We conjecture that the MSO+U theory of the complete binary tree is undecidable. We prove a weaker statement: there is no algorithm which decides this theory and has a correctness proof in zfc. This is because the theory is undecidable, under a set-theoretic assumption consistent with zfc, namely that there exists of projective well-ordering of 2ω of type ω 1. We use Shelah’s undecidability proof of the MSO theory of the real numbers.
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Bojańczyk, M., Gogacz, T., Michalewski, H., Skrzypczak, M. (2014). On the Decidability of MSO+U on Infinite Trees. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_5
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DOI: https://doi.org/10.1007/978-3-662-43951-7_5
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