Model-completeness for a dense linear order in weak monadic second order logic

Deacon Linkhorn

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arXiv · 2209.06655

Model-completeness for a dense linear order in weak monadic second order logic

Deacon Linkhorn

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Abstract

We present a streamlined and (hopefully) accessible proof of the model-completeness of the weak monadic second order version of a dense linear order with left-endpoint but no right-endpoint in a particular finite signature. We also show how this can be used to establish model-completeness of the lattice of finite unions of closed intervals of a dense linear order, i.e. the lattice of closed definable subsets in a (densely ordered) o-minimal structure, in a particularly simple signature (comprising binary functions for union and intersection together with two constant symbols and four unary function symbols).

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BibTeX RIS

Deacon Linkhorn. 2022-09-14. Model-completeness for a dense linear order in weak monadic second order logic. https://arxiv.org/abs/2209.06655

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