Timeline for Does the exact pair phenomenon for partial orders occur in your area of mathematics?
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| Jun 17, 2010 at 12:23 | comment | added | Joel David Hamkins | Thanks for your answer. In the Turing degrees, every increasing sequence has an exact pair, but they are never unique, and indeed I think that every upper bound $b$ forms an exact pair (b,c) with some c. Further, there are upper bounds below $b$, just not below both b and c. So if one were to identify all such pairs in the Turing degrees, the resulting partial order would not have the least-upper-bound property, and may very well continue to exhibit the exact pair property. So I don't really follow your proposal, unless you are just talking about one sequence and one exact pair for it. | |
| Jun 17, 2010 at 8:58 | history | edited | T.. | CC BY-SA 2.5 |
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| Jun 17, 2010 at 8:43 | history | answered | T.. | CC BY-SA 2.5 |