Timeline for Automorphisms of locally finite countable posets
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2011 at 13:11 | comment | added | user16974 | Joel: Is the topology you suggested locally compact? | |
| Sep 19, 2011 at 10:58 | comment | added | Joel David Hamkins | Hollowdead, that particular function does not seem to be a measure, since imagine that a particular point not mentioned by $p$ had three possible images in automorphisms extending $p$, so $U_p$ wouuld be the disjoint union of $U_{p_0}$, $U_{p_1}$ and $U_{p_2}$, but by your proposal these would each have half the measure of $U_p$. So it isn't additive. But in principle, it would seem that there could often be a similar such kind of measure... | |
| Sep 19, 2011 at 9:36 | comment | added | user16974 | Is the application that assigns to every basic open set $U_p$ where $p$ is a finite piece of the automorphism the value $2^{-|p|}$ a measure? $|p|$ is the cardinality of $p$ assumed a minimal generating peice for the basic open set $U_p$. | |
| Sep 19, 2011 at 7:44 | comment | added | user16974 | Joel: Thank you for the enlightning answer. Gerhard: I will ask a more precise question on the same subject. | |
| Sep 19, 2011 at 6:29 | vote | accept | CommunityBot | ||
| Sep 19, 2011 at 1:34 | comment | added | Joel David Hamkins | I am not clear on what is meant. In most contexts I am familiar with, a "connected" poset means a linear order. But it seems unlikely that this is what the OP means, since as I mention the question trivializes in this case. Meanwhile, there are many other interpretations, and so I think the issues needs clarification. | |
| Sep 19, 2011 at 1:27 | comment | added | Gerhard Paseman | Although the original poster has not said so, I am interpreting connected locally finite to mean essentially that (there exists something which is) the smallest connected component of the poset containing the finitely many chosen elements (and) is itself finite as well as convex within the given poset. Even under this restriction, one does not need large antichains but only infinitely many of them to construct examples with uncountable automorphism group. Gerhard "Ask Me About System Design" Paseman, 2011.09.18 | |
| Sep 19, 2011 at 1:25 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Sep 19, 2011 at 1:19 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Sep 19, 2011 at 1:11 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |