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

interpretation of z in b + sde 149y> ex {x 1 ,...,x n } if (∀x)(x ex ϕ), where ϕ is x = x 1 ∨ ...∨ x = x n .The third claim is proved by induction on n. Let x be given, and letA(x,y 1 ,...,y n−1 ), where this is considered vacuously true if n = 1. Let x ′ >x,y 1 ,...,y n−1 . Obviously, x ′ >ϕ, where ϕ is x ≠ x. ByDE,(∃y n )(¬y n ex ϕ),(∃y n )(¬y n ≤ x,y 1 ,...,y n−1 ∧ y n ∼⊘),(∃y n )(¬y n ≤ x ∧ y n ≠ y 1 ,...,y n−1 ∧ y n ∼⊘),A(x,y 1 ,...,y n ).Lemma 8.2 Let ϕ be a formula of L(>, ≫, =) in which u, v do notappear. Suppose y> ex ϕ, where (∀u, v)(ϕ[x/u]∧ϕ[x/v]→ ¬u