English

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

Logic 2022-09-15 v1

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).

Keywords

Cite

@article{arxiv.2209.06655,
  title  = {Model-completeness for a dense linear order in weak monadic second order logic},
  author = {Deacon Linkhorn},
  journal= {arXiv preprint arXiv:2209.06655},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2207.07884

R2 v1 2026-06-28T01:17:19.957Z