MIT24_241F09_lec13 - Logic I Session 13 Plan Damien on...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 C-SD ↓ Γ ∪ { ∼ P } ⊆ a MC-SD set Γ * ↓ If Γ * is MC-SD then Γ * is TF-C ↓ Γ ∪ { ∼ P } ⊆ a TF-C set Γ * ↓ Γ ∪ { ∼ P } is TF-C ↓ Γ ⊭ P Compactness A cool result of completeness: Compactness : Γ is TF-C iff every ¡nite subset of Γ is TF-C. So: a set Γ is TF-IC only if a ¡nite subset of Γ is TF-IC. 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, left-to-right: If Γ is TF-C, then every ¡nite subset of Γ is TF-C. 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, right-to-left: If every ¡nite subset of Γ is TF-C, then Γ is TF-C....
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.

Page1 / 8

MIT24_241F09_lec13 - Logic I Session 13 Plan Damien on...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online