We prove a number of dualities between posets and (pseudo)bases of open sets in locally compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic sublattices are finitely axiomatizable. (2) Relatively compact basic subsemilattices are those omitting certain types. (3) Compact clopen pseudobasic posets are characterized by separativity. We also show how to obtain the tight spectrum of a poset as the Stone space of a generalized Boolean algebra that is universal for tight representations.

Additional Metadata
Keywords Boolean algebra, First order axiomatization, Locally compact topology, Relatively compact basis, Separative poset, Stone space, Tight spectrum/representation
Persistent URL dx.doi.org/10.4115/jla.2018.10.2
Journal Journal of Logic and Analysis
Citation
Bice, T. (Tristan), & Starling, C. (2018). Locally compact stone duality. Journal of Logic and Analysis, 10. doi:10.4115/jla.2018.10.2