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Jan 25, 2010 at 15:00 comment added Joel David Hamkins Very Nice. This shows that Compactness provides a clean reduction of Completeness for uncountable languages to finite languages. So if we have Compactness, we can avoid the transfinite issues in Completeness that arise for uncountable languages (which are sometimes difficult issues for students).
Jan 25, 2010 at 8:52 history answered Michał Kukieła CC BY-SA 2.5