The covering lemma for L[U]

Dodd, A.; Jensen, Ronald Björn

doi:10.1016/0003-4843(82)90018-3

Cited by 35 publications

(15 citation statements)

References 3 publications

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“…Note that by (3) we know that If is rank rj -1 complete. Statements (3)(4)(5) and (7) all follow immediately from the induction hypothesis. To see (6), note that for all /i, F» is obtained by augmenting the functions in F° = i$M by adding the function si'(a, ft, y) for rj' < y.…”

Section: Proof We Define the Iterated Ultrapower I P :M^-m V By Recumentioning

confidence: 92%

The core model for sequences of measures. I

Mitchell

1984

Math. Proc. Camb. Phil. Soc.

113

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The model K() presented in this paper is a new inner model of ZFC which can contain measurable cardinals of high order. Like the model L() of [14], from which it is derived, K() is constructed from a sequence of filters such that K() satisfies for each (α, β) ε domain () that (α,β) is a measure of order β on α and the only measures in K() are the measures (α,β). Furthermore K(), like L(), has many of the basic properties of L: the GCH and ⃟ hold and there is a definable well ordering which is on the reals. The model K() is derived from L() by using techniques of Dodd and Jensen [2–5] to build in absoluteness for measurability and related properties.

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Section: Proof We Define the Iterated Ultrapower I P :M^-m V By Recumentioning

confidence: 92%

The core model for sequences of measures. I

Mitchell

1984

Math. Proc. Camb. Phil. Soc.

113

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“…The basic result is that such sequences are, except on a bounded set, independent of the particular covering set used to obtain the indiscernibles. The applications to the singular cardinal hypothesis are given in section 3, and some open problems are stated in section 4.…”

Section: 1mentioning

confidence: 99%

“…The covering lemma for one measure [2,3] asserts that if 0 † does not exist then any uncountable set x of ordinals is contained in a set y such that |y| = |x| and either y ∈ K (where K = L[µ] if it exists and K is the Dodd-Jensen core model otherwise) or else y ∈ L[µ, C] where C is a Prikry sequence for the measure µ. Furthermore the Prikry sequence C is unique up to initial segments: any other Prikry sequence over L[µ] is contained in C except for a finite set.…”

Section: 1mentioning

confidence: 99%

Indiscernible sequences for extenders, and the singular cardinal hypothesis

Gitik

Mitchell

1996

Annals of Pure and Applied Logic

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“…The definition of Prikry forcing with a normal ultrafilter U over κ, denoted by P (U), uses the existence of a measurable cardinal. Later it was shown by Dodd and Jensen [7] that if there is a forcing notion which preserves all cardinals and changes cofinalities, there is an inner model with a measurable cardinal.…”

Section: Introductionmentioning

confidence: 99%