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Unformatted text preview: Logic I  Session 13 Plan Damien on psets Quick summary of completeness Compactness Limitations of SL Intro to PL Completeness P { P } is CSD { P } a MCSD set * If * is MCSD then * is TFC { P } a TFC set * { P } is TFC P Compactness A cool result of completeness: Compactness : is TFC iff every nite subset of is TFC. So: a set is TFIC only if a nite subset of is TFIC. So, intuitively, theres no TF inconsistency that you need an innite number of SL sentences to get! Lets prove compactness by proving each direction. Compactness First, lefttoright: If is TFC, then every nite subset of is TFC. If there were a subset  such that no TVA m.e.m.  true, then there would be no TVA m.e.m. true. Now, righttoleft: If every nite subset of is TFC, then is TFC....
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 Fall '10
 DerekAllen
 Philosophy

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