Timeline for When forcing with a poset, why do we order the poset in the order that we do?
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| Apr 15, 2010 at 12:37 | comment | added | Joel David Hamkins | This idea has some affinity with the Boolean algebra approach, since the canonical map of the poset P into its Boolean algebra completion B as the regular open algebra of P (the collection of all regular open subsets of P) take a condition p essentially to the lower cone { q | q $\leq$ p } of all conditions below p. (One should actually use the interior of the closure of this set.) And since stronger conditions have smaller lower cones, the order turns into subset as you mention. | |
| Mar 29, 2010 at 0:41 | history | answered | Uri Andrews | CC BY-SA 2.5 |