henkin_a - Part (a) of Hunters Proof of Henkins...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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))...
View Full Document

Ask a homework question - tutors are online