终极L（数学论文）一 (14-6)

normal ultrafilter on κ₀.denoted by U in what follows. We may use reflection to show the existence of a κ'₀＜κ₀ belonging to any fixed member of U，such that 〈κ'₀，κ₀，κ₁ . . .〉，together with a certain family F₀ of elementary embeddings，witness ω-tremendousness of κ.Then we can repeat this procedure to find a κ'₁ belonging to the same fixed member of U such that κ'₀＜κ'₁＜κ₀，such that 〈κ'₀，κ'₁，κ₀，κ₁，. . .〉，together with a certain family F₁ of elementarv embeddings，witness

ω-tremendousness of κ.We can continue in this way，and we can also ar- range things so that there is a sequence of embeddings，jₙ： Vκ'ₙ₋₁ ≺ Vκ'ₙ with critical point κ'₀ for all n＞1，which can be chosen by induc-tion，such that for each n＞1，jₙ coheres with jₘ for all m such that 1＜m＜n，and the embeddings from Fₙ that have critical sequence beginning with 〈κ'₀，κ'₁，. . .，κ'ₙ₋₂〉can be chosen so as to be coherent with jₙ. In this way we obtain a sequence 〈κ'ₙ：n＜ω〉and a sequence of embeddings jₙ with the previously stated properties. The existence of such a pair of sequences for any given element of U yields the claimed result. ▢

Theorem 2.4.Suppose thαt κ is αn l2 cαrdinαl. Then there is α nor-mαl ultrαfilter U on κ concentrαting on the hyper-tremendous cαrdinαls.

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