Timeline for Automorphisms of locally finite countable posets
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2011 at 18:16 | comment | added | Joel David Hamkins | Ali, there is a nice probability measure on the poset of my answer, if you think of each swap as a coin flip. Gerhard, I added an example with many diamonds, whose automorphism group is countably infinite. | |
| Sep 19, 2011 at 18:12 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Added Gerhard's example; added 30 characters in body
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| Sep 19, 2011 at 17:42 | comment | added | user16974 | Joel: do you mind keeping in touch for the question of measure? | |
| Sep 19, 2011 at 17:33 | comment | added | Gerhard Paseman | I had in mind a minor variation of your example, but with essentially the same characteristics, and I used the word diamond in the answer I was typing to this question. Also, I stand by my existence claim of posets wanted by the user that have countably infinite automorphism group, but they seem to be Z or minor variations thereupon. I hope to come up with one that also includes a diamond, but that is more of a challenge. Perhaps you recall an example that includes a diamond with |Aut(P)|= omega ? Gerhard "Needs Coffee To Get Fancy" Paseman, 2011.09.19 | |
| Sep 19, 2011 at 16:58 | comment | added | Joel David Hamkins | Gerhard, was this the poset to which you had alluded to in the other post? | |
| Sep 19, 2011 at 16:57 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 29 characters in body
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| Sep 19, 2011 at 16:57 | comment | added | Gerhard Paseman | I guess I will have to take a typing to class to match your speed, Joel. One can add other elements and features to make a poset with a countably infinite automorphism group, but such constructions are a little more intricate; until more motivation is provided, I do not see the need for providing such. Gerhard "Ask Me About System Design" Paseman, 2011.09.19 | |
| Sep 19, 2011 at 16:55 | vote | accept | CommunityBot | ||
| Sep 19, 2011 at 16:47 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |