16 lines
396 B
Plaintext
16 lines
396 B
Plaintext
Applications of compactness theorem:
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2-colorability of graphs
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Goal: Given a graph G=(V,E) it is 2-colorable iff every finite subset of G is 2-colorable.
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Proof outline:
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Given a graph G=(V,E) construct a set \Sigma of wffs such that
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G is 2-colorable
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iff (step 1)
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\Sigma is satisfiable.
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iff
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(by CT) \Sigma is finitely satisfiable
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iff (step 2)
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Each finite subset of G is 2-colorable.
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