终极L（数学论文）一 (14-13)

Vλ₊₂ ≺ Vλ₊₂，then there is a normal ultrafilter U concentrating on a sequence 〈κα：α＜κ〉 which witnesses that κ is hyper-enormous*.In[6]，Gabriel Goldberg has also shown，using iterated collapse forcing，that if the existence of such an embedding is consistent with ZF then it is also consistent with Vλ being well-orderable (using a well-ordering where if m＜n and 〈κ'ᵢ：i ∈ ω〉is the critical sequence of j ，the map jⁿ⁻ᵐ maps the restriction of the well-ordering to Vκ'ₘ₊₁ \ Vκ'ₘ to the restriction of the well-ordering to Vκ'ₙ₊₁ \ Vκ'ₙ).

So suppose the conjunction of these two hypotheses，in ZF，and let κ be the critical point of the embedding and let S be the sequence 〈κα：α＜κ〉 mentioned before. For each α＜κ，let Eα be the equivalence relation on [κα]ω which holds of two sets of ordinals less than κα whose elements in order constitute two sequences of countably infinite length，if and only if the two seguences in question have the same tail. There is a sequence 〈Cα：α＜κ〉 such that for each α＜κ，Cα is a choice set for the equivalence classes of Eα，and for each pair (α，β) with

α＜β，when one is choosing an elementary embedding j' from a fixed family of embeddings witnessing the hyper-enormous*ness of κ，one can without loss of generality choose it so that j'(Cα)＝Cᵦ. Then using the embedding j one can extend this to a family of choice sets 〈Cα：α＜λ〉，such that if α ＜β ＜κ'ₙ then an elementary embedding j' can be chosen which is part of a fixed family of embeddings witnessing the hyper-enormous*ness of κ'ₙ，such that j'(Cα)＝Cᵦ.

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。