Access Millions of academic & study documents

Suppose towards a contradiction that there is a proof of in t

Content type
User Generated
School
Jomo Kenyatta University of Agriculture and Technology
Showing Page:
1/2
(a) Suppose towards a contradiction that there is a proof of πρ in T,
with code m, so by the hypotheses,
Q ` Proof
π,T
(pρq,m).
Taking y = m and appealing to the hypothesis and basic facts about
Q, we get that
Q ` (y)[Proof
π,T
(pρq,y) & (u yRefute
π,T
(pρq,u)]; thus with
(4C-4), Q ` ¬ρ, hence T ` πρ), i.e., T ` ¬π(ρ), contradicting the
assumed consistency of T.
(b) Suppose now that there is a proof in T of ¬π(ρ), hence a proof of
πρ), and let m be its code. We know that
Q ` Refute
π,T
(pρq,m),
among other things. To prove

Sign up to view the full document!

lock_open Sign Up
Showing Page:
2/2

Sign up to view the full document!

lock_open Sign Up
Unformatted Attachment Preview
(a) Suppose towards a contradiction that there is a proof of πρ in T, with code m, so by the hypotheses, Q ` Proof π,T(pρq,∆m). Taking y = ∆m and appealing to the hypothesis and basic facts about Q, we get that Q ` (∃y)[Proof π,T(pρq,y) & (∀u ≤ y)¬Refuteπ,T(pρq,u)]; thus with (4C-4), Q ` ¬ρ, hence T ` π(¬ρ), i.e., T ` ¬π(ρ), contradicting the assumed consistency of T. (b) Suppose now that there is a proof in T of ¬π(ρ), hence a proof of π(¬ρ), and let m be its code. We know that Q ` Refuteπ,T(pρq,∆m), among other things. To prove (4C-5) (∀y)[Proof ? ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.
Studypool
4.7
Indeed
4.5
Sitejabber
4.4