数学联邦政治世界观
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终极L(数学论文)一 (14-12)

Definition5.1.Suppose that α is a limit ordinal such that α>0,and that〈κᵦ:β<α〉together with a family F of elementary embeddings witness that κ is α-tremendous,with just one embedding in the family F witnessing α-tremendousness for each finite sequence of ordinals less than α.Suppose that,given any ω-sequence of ordinals〈βᵢ:i<ω〉less than α. there is an elementary embedding j:Vλ₊₁ ≺ Vλ₊₁ with critical sequence 〈κᵦᵢ:i<ω〉,obtained by gluing together the obvious ω-sequence of embeddings from F,where λ:=supₙ∈ω κᵦₙ .Then the cardinal κ is said to be α-enormous*.

Definition 5.2.Suppose that a cardinal κ is κ-enormous*.Then κ is said to be hyper-enormous*.

In this section we wish to prove the following theorem.

Theorem 5. is not consistent ωith ZF thαt there exists αn ordinαl λ αnd α non-triυiαl elementαry embedding j:Vλ₊₂ ≺ Vλ₊₂.

Proof.The same reasoning that shows that every I2 cardinal κ has a normal ultrafilter U concentrating on the hyper-tremendous cardinals,also shows in ZF that if κ is a critical point of an elementary embedding

NEW LARGE-CARDINAL AXIOMS AND THE ULTIMATE-L PROGRAM 9

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