Introduction to I0: Elementary Embeddings
نویسنده
چکیده
The added assumption for the critical point is necessary to put I0 in the same branch of the other rank-into-rank axioms. If j witness I0, in fact, j Vλ+1 witness I1, and so λ is the supremum of the critical sequence. Note that if I0 is true, then L(Vλ+1) 2 AC, because otherwise we could use Kunen’s Theroem to prove that there is no elementary embedding. One of the big peculiarities of I0 is its affinity with AD in L(R) (we’ll se these in Chapter Five). In fact, this similarities are grounded on some basic ones between L(Vλ+1) and L(R) themselves. Lemma 0.2. There exists a definable surjection Φ : Ord× Vλ+1 L(Vλ+1).
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