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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 \(K\).

03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
Full Text: DOI arXiv
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[2] The core model iterability problem 8 (1996) · Zbl 0864.03035
[3] DOI: 10.1016/0168-0072(94)00021-T · Zbl 0821.03023
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[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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