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Sep 29, 2011 at 17:46 history edited user16974 CC BY-SA 3.0
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Sep 29, 2011 at 17:32 history edited user16974 CC BY-SA 3.0
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Sep 29, 2011 at 15:18 answer added David timeline score: -2
Sep 29, 2011 at 13:28 comment added user16974 Yes that is true, but I am not very well aware of poset terminology.
Sep 29, 2011 at 12:46 vote accept CommunityBot
Sep 29, 2011 at 9:41 answer added Colin Reid timeline score: 2
Sep 29, 2011 at 9:26 history edited Colin Reid
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Sep 29, 2011 at 9:25 comment added Emil Jeřábek I still do not quite understand it. Every singleton is an antichain, so is condition 1 simply saying that every maximal chain is upwards and downwards cofinal in the poset? Since the poset is countable, isn’t this equivalent to the poset being upwards and downwards directed?
Sep 29, 2011 at 6:28 history edited user16974 CC BY-SA 3.0
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Sep 29, 2011 at 4:50 comment added user16974 Joel: I edited the question.
Sep 29, 2011 at 4:50 history edited user16974 CC BY-SA 3.0
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Sep 29, 2011 at 0:46 comment added Joel David Hamkins The quantifiers in your hypothesis are not clear. Do you mean to assume that your partial order, in addition to being locally finite, countable and connected, has the covering property for every pair (A,C) of a maximal chain and maximal antichain? And when you say A is covered by Past(x) and Future(x), do you mean that the family of pasts alone covers A and also the family of futures alone covers A? Or do you mean that one might possibly need both futures and pasts from C to cover A?
Sep 28, 2011 at 19:21 comment added user16974 It is related to a quantization procedure on a family of isomorphic causal sets, which are locally finite countable connected posets.
Sep 28, 2011 at 18:53 comment added André Henriques I dont understand the title of the question: what are we quantizing?
Sep 28, 2011 at 18:22 history asked user16974 CC BY-SA 3.0