Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_ Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

12.07.2015 Views

162 concept calculus: much better thanproof Let n, ϕ be as given. We can assume that the free variables of ϕ areamong x 1 ,...,x m , y 1 ,...,y n , z, which are distinct variables, and distinct fromx,w.Fix x, x 1 ,...,x m such that the implication fails. Let x ′ >x, x 1 ,...,x m . LetA(x ′ a 1 ,...,a m+n+1 ). By Lemma 8.7, let v be such that(∀y 1 ,...,y n

162 concept calculus: much better thanproof Let n, ϕ be as given. We can assume that the free variables of ϕ areamong x 1 ,...,x m , y 1 ,...,y n , z, which are distinct variables, and distinct fromx,w.Fix x, x 1 ,...,x m such that the implication fails. Let x ′ >x, x 1 ,...,x m . LetA(x ′ a 1 ,...,a m+n+1 ). By Lemma 8.7, let v be such that(∀y 1 ,...,y n

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