终极L（数学论文）二 (7-3)

Suppose that κ is ω-enormous as witnessed by a sequence 〈κₙ：n＜ω〉，where clearly we may assume without loss of generality that the latter sequence is in HOD，and we will do so. Then we may consider all the sets ofordinals of the form j”λ where λ：＝sup{κₙ：n ∈ ω} for some sequence 〈κₙ：n ∈ ω〉 with the properties previously described，and j is an elementary embedding Vλ₊₁ ≺ Vλ₊₁ with critical sequence〈κₙ：n ∈ ω〉. Some of these sets of ordinals will be members of HOD. We define Ultimate-L to bethe smallest enlargement of L containing every member of a proper-class-length sequence of such set of ordinals in HOD， obtained in this way from ω-enormous cardinals κ，with exactly one such set of ordinals j” λ in the sequence for every possible value of λ. It will follow from the results of this section together with known results about the Ultimate-L Coniecture that Ultimate-L so defined does not in fact depend on the choice of the sequence. In this model，there will indeed exist at least one elementary embedding j：Vλ₊₁ ≺ Vλ₊₁ with critical sequence 〈κₙ：n ∈ ω〉，for every possible critical sequence in HOD arising from an embedding partially witnessing α-enormousness of some cardinal in V. The necessary elementary embedding within the model can be constructed using similar arguments to those of Section

数学联邦政治世界观提示您：看后求收藏（同人小说网http://tongren.me），接着再看更方便。