#Logic

3 messages · Page 1 of 1 (latest)

mint valley
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Let A be not tautology. Let L be Hilbert’s system and we gonna add A as an axioms so we get the following axioms:

1. $A_1 :A\to (B\to A)$
\ $2. A_2:(A\to (B\to C))\to ((A\to B)\to (A\to C))$\
3. $A_3:(\lnot B\to \lnot A)\to ((\lnot B\to A)\to B)$\
4. A \

Prove that in the new system there exists some B such that B and not B are provable.

royal lanceBOT
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