终极L（数学论文）一 (14-14)

This allows one to construct a choice set C for the corresponding equivalence relation E on [λ]ω. The method is as follows. Given an X ∈ [λ]ω， it follows from our stated assumptions that one may find an X' ∈ Vκ'ₙ for any given n＞0 such that X' ∈ [ρ]ω for a ρ of cofinality ω between κ'ₙ₋₁ and κ'ₙ and an embedding ex.ₙ：Vᵨ₊₁ ≺ Vλ₊₁ which carries a sequence of hyper-enormous* cardinals cofinal in ρ to the critical sequence of j or a tail thereof，such that ex，ₙ(X')＝X. This can be used together with the sequence of choice sets 〈Cα：α＜λ〉to choose a member of the equivalence class of X，depending on n. Using the relation mentioned earlier between the different choice sets Cα，one can argue that this data can be chosen in such a way that the function mapping n to the chosen member of the equivalence class of X is in fact eventually constant，and that a choice set for the equivalence relation E can be constructed in this way.

However，this gives rise to a contradiction using the method of proof of Kunen’s inconsistency theorem. And this contradiction was obtained

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