Working in ZF+AD alone, we prove that every set of ordinals with cardinality at
least Θ can be covered by a set of ordinals in HOD of
K(ℝ) of the same cardinality, when there is no inner model
with an ℝ-complete measurable cardinal. Here ℝ is the set
of reals and Θ is the supremum of the ordinals which are the
surjective image of ℝ.
Publié le : 2010-10-15
Classification:
descriptive set theory,
determinacy,
fine structure,
03E15,
03E45,
03E60
@article{1285765797,
author = {Cunningham, Daniel W.},
title = {A Covering Lemma for HOD of K($\mathbb{R}$)},
journal = {Notre Dame J. Formal Logic},
volume = {51},
number = {1},
year = {2010},
pages = { 427-442},
language = {en},
url = {http://dml.mathdoc.fr/item/1285765797}
}
Cunningham, Daniel W. A Covering Lemma for HOD of K(ℝ). Notre Dame J. Formal Logic, Tome 51 (2010) no. 1, pp. 427-442. http://gdmltest.u-ga.fr/item/1285765797/