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Sep 2, 2014 at 18:48 comment added Michał Kukieła @PaulTaylor I am not sure what you are asking for, but perhaps you will be interested in another paper of Schroeder that is not behind a paywall: csi.uottawa.ca/ordal/papers/schroder/FINSURVE.html (I also recommend his book). A recent paper of Szymik (dx.doi.org/10.1007/s11083-014-9332-x or in preprint version arxiv.org/abs/1210.6496) gives some insight into the "meaning" of the "strong fixed point property" described in your answer, my answer and Schroeder's paper.
Sep 2, 2014 at 16:06 comment added Paul Taylor (All the other references here are behind a paywall but) the Schroder paper contains some interesting arguments that are similar to ones that have been used in domain theory. Unfortunately, the discussion on this page is an example of the way that pure mathematicians and computer scientists (by which I mean the inhabitants of university buildings so called - we are all mathematicians) talk past one another. I have given a similar theorem and its background from computer science - what it the background for these fixed point results for posets in pure mathematics (departments)?
Aug 31, 2014 at 18:52 history answered Gejza Jenča CC BY-SA 3.0