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arXiv · 1502.04578

The MSO+U theory of (N, <) is undecidable

Mikołaj Bojańczyk·Paweł Parys·Szymon Toruńczyk
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Abstract

We consider the logic MSO+U, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the logic is undecidable on infinite words, i.e. the MSO+U theory of (N,<) is undecidable. This settles an open problem about the logic, and improves a previous undecidability result, which used infinite trees and additional axioms from set theory.

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Mikołaj Bojańczyk, Paweł Parys, Szymon Toruńczyk. 2015-02-16. The MSO+U theory of (N, <) is undecidable. https://arxiv.org/abs/1502.04578

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