0. I advise against reading my PhD thesis. Unfortunately there are some errors and the exposition is unclear in places. The significant results have all made it into papers by now, usually in an improved form.
R. Egrot and R. Hirsch. Completely representable lattices. Algebra Universalis 67, 205-217, 2012
The statement of proposition 2.16 is slightly incorrect in the published version. This error is corrected in the arXiv version.
R. Egrot. Representable posets. J. Appl. Log. 16, 60-71, 2016
In the introduction and the discussion following corollary 2.9 the question of whether the class of representable semilattices can be finitely axiomatized is raised as open. In fact this was settled conclusively in the negative by Kearnes (The Class of Prime Semilattices is Not Finitely Axiomatizable, Semigroup Forum 55, 133-134, 1997).
R. Egrot. Closure operators, frames, and neatest representations. Bulletin of the Australian Mathematical Society 96, 361-373, 2017
The material in the first three sections is simplified and superseded by my preprint Categories of frame-completions and join-specifications.
R. Egrot. Categories of frame-completions and join-specifications.
It's been brought to my attention that several of the results here are reformulations and applications of the theory of subcanonical coverages. This paper is not currently submitted anywhere, and needs to be substantially rewritten to extract the novel parts and place them in their proper context. Most likely this would ultimately result in an essentially new paper superseding this one, but I haven't found the time to do the necessary work yet (and indeed I may never get round to it).