14 February 2020, Cool Logic, Joseph McDonald

In this talk, I will exposit the fundamental ideas underlying my current independent research project with Nick Bezhanishvili, in which I am attempting to give a choice-free topological representation of ortholattices. The standard topological representation of ortholattices, distributive lattices, and Boolean algebras, relies upon a nonconstructive choice principle, equivalent to the Boolean prime ideal theorem - which guarantees the existence of sufficiently many ultrafilters. My topological representation of ortholattices combines Bimbo's 2007 orthospace approach to choice-dependent Stone duality for ortholattices with Bezhanishvili and Holliday's 2020 spectral space approach to choice-free Stone duality for Boolean algebras. My aim for this talk is to give a gentle and welcoming overview of my research project and its surrounding subject matter.