Logicandapplications2023/class_10_29082023/summary.txt

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2023-08-29 14:58:24 +05:30
Applications of compactness theorem:
2-colorability of graphs
Goal: Given a graph G=(V,E) it is 2-colorable iff every finite subset of G is 2-colorable.
Proof outline:
Given a graph G=(V,E) construct a set \Sigma of wffs such that
G is 2-colorable
iff (step 1)
\Sigma is satisfiable.
iff
(by CT) \Sigma is finitely satisfiable
iff (step 2)
Each finite subset of G is 2-colorable.