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A universal extender model without large cardinals in \(V\). (English) Zbl 1069.03046
Summary: We construct, assuming that there is no inner model with a Woodin cardinal but without any large cardinal assumption, a model \(K^c\) which is iterable for set length iterations, which is universal with respect to all weasels with which it can be compared, and (assuming GCH) is universal with respect to set sized premice.

MSC:
03E45 Inner models, including constructibility, ordinal definability, and core models
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References:
[1] Deconstructing inner model theory 67 pp 721– (2002)
[2] The core model iterability problem 8 (1996) · Zbl 0864.03035
[3] Set theory (1978)
[4] Fine structure and iteration trees 3 (1994) · Zbl 0805.03042
[5] Addendum to ”A new fine structure for higher core models” (1997)
[6] DOI: 10.1016/S0168-0072(01)00113-0 · Zbl 1017.03029
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