This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Logic I  Session 13 Plan Damien on psets Quick summary of completeness Compactness Limitations of SL Intro to PL Completeness Γ ⊬ P ↓ Γ ∪ { ∼ P } is CSD ↓ Γ ∪ { ∼ P } ⊆ a MCSD set Γ * ↓ If Γ * is MCSD then Γ * is TFC ↓ Γ ∪ { ∼ P } ⊆ a TFC set Γ * ↓ Γ ∪ { ∼ P } is TFC ↓ Γ ⊭ P Compactness A cool result of completeness: Compactness : Γ is TFC iff every ¡nite subset of Γ is TFC. So: a set Γ is TFIC only if a ¡nite subset of Γ is TFIC. So, intuitively, there’s no TF inconsistency that you need an in¡nite number of SL sentences to get! Let’s prove compactness by proving each direction. Compactness First, lefttoright: If Γ is TFC, then every ¡nite subset of Γ is TFC. If there were a subset Γ such that no TVA m.e.m. Γ true, then there would be no TVA m.e.m. Γ true. Now, righttoleft: If every ¡nite subset of Γ is TFC, then Γ is TFC....
View
Full
Document
This note was uploaded on 01/25/2012 for the course PHIL 201H1F taught by Professor Derekallen during the Fall '10 term at University of Toronto.
 Fall '10
 DerekAllen
 Philosophy

Click to edit the document details