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Core models in the presence of Woodin cardinals. (English) Zbl 1109.03064
Summary: Let \(0<n<\omega\). If there are \(n\) Woodin cardinals and a measurable cardinal above, but \(M^\#_{n+1}\) does not exist, then the core model \(K\) exists in a sense made precise. An iterability inheritance hypothesis is isolated which is shown to imply an optimal correctness result for \(K\).

MSC:
03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
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References:
[1] Core models with more Woodin cardinals 67 pp 1197– (2002) · Zbl 1012.03055
[2] The core model iterability problem 8 (1996) · Zbl 0864.03035
[3] DOI: 10.1016/0168-0072(94)00021-T · Zbl 0821.03023
[4] Kc without large cardinals in V 69 pp 371– (2004)
[5] DOI: 10.1090/S0002-9947-99-02411-3 · Zbl 0928.03059
[6] DOI: 10.2307/421159 · Zbl 0835.03017
[7] Fine structure and iteration trees 3 (1994) · Zbl 0805.03042
[8] Iterates of the core model 71 pp 241– (2006)
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