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).
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