Iterates of the core model
Schindler, Ralf
J. Symbolic Logic, Tome 71 (2006) no. 1, p. 241-251 / Harvested from Project Euclid
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Let N be a transitive model of ZFC such that ω N ⊂ N and 𝒫(ℝ) ⊂ N. Assume that both V and N satisfy “the core model K exists.” Then KN is an iterate of K, i.e., there exists an iteration tree 𝒯 on K such that 𝒯 has successor length and ℳ𝒯∞ = KN. Moreover, if there exists an elementary embedding π : V → N then the iteration map associated to the main branch of 𝒯 equals π ↾ K. (This answers a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that 𝒫(ℝ) ⊂ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals.
Publié le : 2006-03-14
Classification:  set theory,  core models,  large cardinals,  03E15,  03E45,  03E55 
@article{1140641172,
     author = {Schindler, Ralf},
     title = {Iterates of the core model},
     journal = {J. Symbolic Logic},
     volume = {71},
     number = {1},
     year = {2006},
     pages = { 241-251},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1140641172}
}

Schindler, Ralf. Iterates of the core model. J. Symbolic Logic, Tome 71 (2006) no. 1, pp.  241-251. http://gdmltest.u-ga.fr/item/1140641172/