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Unformatted text preview: Part (a) of Hunters Proof of Henkins Completeness Theorem for PS Branden Fitelson 02/21/07 The first part of Henkins completeness proof involves proving the following seven theorem schemas . 1. PS A A 2. PS A (B A) 3. PS (A (B C)) ((A B) (A C)) 4. PS A (A B) 5. PS A ( B (A B)) 6. PS (A B) ((A B) A) 7. PS ( A B) (( A B) A) We have already seen a proof of (1). (2) and (3) are (PS1) and (PS2). So, we just need proofs of the four theorem schemas (4)(7). Here is a sketch (!) of one such proof (4 goals in boldface ). Exercise: figure out the substitution instances of the formulas (listed on the right) required to generate each MP step. PS1 A (B A) PS2 A (B C)) ((A B) (A C)) PS3 ( A B) (B A) 1. A (B (C B)) [MP, PS1, PS1] 2. ((A (B C)) (A B)) ((A (B C))...
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- Spring '07