Timeline for Terminology for posets.
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 18, 2010 at 23:45 | comment | added | Joel David Hamkins | It's my pleasure. | |
| Dec 18, 2010 at 15:46 | vote | accept | Jeff Strom | ||
| Dec 18, 2010 at 15:26 | comment | added | Joel David Hamkins | In that case, and in light of the other things you have said, you have a well-founded tree (or forest) of height at most $\omega$. For partial orders, a tree is a partial order in which the predecessors of every node are linearly ordered. Combined with well-foundedness, this means that the predecessors of every node are well-ordered, and so the tree arranges itself naturally into levels. Your immediate predecessor assumption means that every node is on a finite level (so the total height is at most $\omega$). | |
| Dec 18, 2010 at 14:16 | comment | added | Jeff Strom | I tried to clarify! Basically, the poset should look like a forest (in the sense of graph theory). | |
| Dec 18, 2010 at 14:04 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Dec 18, 2010 at 13:57 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Dec 18, 2010 at 13:48 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |