Timeline for Does every locally finite acyclic directed set embed into a linear order locally isomorphic to the integers? (Edit: extend, not merely embed.)

8 events

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Sep 26, 2013 at 8:38	history	edited	Ben	CC BY-SA 3.0	added 99 characters in body
Sep 26, 2013 at 7:25	comment	added	Ben		Joel, that's a helpful observation, since it allows you to begin with an arbitrary enumeration and try to use some sort of inductive procedure.
Sep 26, 2013 at 3:00	comment	added	Joel David Hamkins		Incidentally, you can reduce to the countable case, since the connected components of $S$ are each countable, and you can treat each connected component separately, afterwards merging these discrete orders into one giant discrete order. (There is a complication when most of the discrete orders arising have a minimal but no maximal element, or conversely, but this can be handled by allowing those bottom parts to overlap.)
Sep 25, 2013 at 23:51	comment	added	Joel David Hamkins		Your edit makes this an extremely interesting question!
Sep 25, 2013 at 19:58	comment	added	Joel David Hamkins		By the way, these kinds of orders are called discrete orders, a linear order where every non-least point has an immediate predecessor and every non-greatest point has an immediate successor.
Sep 25, 2013 at 19:45	history	edited	Ben	CC BY-SA 3.0	added 379 characters in body
Sep 25, 2013 at 12:53	answer	added	Joel David Hamkins		timeline score: 1
Sep 25, 2013 at 8:27	history	asked	Ben	CC BY-SA 3.0