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 -complete
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(Definition)
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A structured set $S$ (typically a filter or a Boolean algebra) is $\kappa$ complete if, given any $K\subseteq S$ with $|K|<\kappa$ $\bigcap K\in S$ It is complete if it is $\kappa$ complete for all $\kappa$
Similarly, a partial order is $\kappa$ complete if any sequence of fewer than $\kappa$ elements has an upper bound within the partial order.
A $\aleph_1$ complete structure is called countably complete.
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" -complete" is owned by Henry.
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(view preamble | get metadata)
See Also: filter, Boolean algebra
| Other names: |
kappa-complete, kappa complete |
| Also defines: |
countably complete |
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Cross-references: upper bound, sequence, partial order, complete, Boolean algebra, filter
This is version 8 of  -complete, born on 2002-07-29, modified 2003-01-31.
Object id is 3230, canonical name is KappaComplete2.
Accessed 6029 times total.
Classification:
| AMS MSC: | 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers) |
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Pending Errata and Addenda
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