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Unformatted text preview: induction on derivations. In doing so, formulate the principle of normal induction on derivations as a conditional statement. Then prove this conditional with what you have formulated in 3b). (Hint: an analogous proof is given—as a subproof—in the proof of theorem 1.1.8. Also, the conditional statement that expresses the principle of normal induction on derivations is a complicated one. See theorem 1.1.3 for the analogous statement for induction on propositions.) 4. (6 points) Do exercise 1 on page 47. 5. (8 points) Deﬁne a consistent set Γ such that (a) Γ has only one maximally consistent set containing it. (b) There is a natural number k such that all propositions in Γ have rank less than or equal to k . 1 Your proof that the set you deﬁne satisﬁes (a) and (b) can use any of the facts proven about maximally consistent sets in section 1.5. 6. (6 points) Do exercise 6 on page 48. 2...
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This document was uploaded on 02/08/2011.
- Winter '09