Choice-free representation of ortholattices
Kentarô Yamamoto · eScholarship (California Digital Library) · 2020
We continue the study of the topological duality for ortholattices started by Goldblatt (1975), comparing it with the choice-free duality sketched in Bezhanishvili and Holliday (2019), which is examined here in detail.In both cases, we characterize the duals of ortholattices and extend the duality categorically with the suitable morphisms.Afterwards, we identify a separate, first-order definable way in which the original ortholattice may be obtained from its choice-free dual.An application of this is a nontrivial characterization of the duals of orthomodular lattices.