Abstract.
Jensen's celebrated Covering Lemma states that if 0# does not exist, then for any uncountable set of ordinals X, there is a Y∈L such that X⊆Y and |X| = |Y|. Working in ZF + AD alone, we establish the following analog: If ℝ# does not exist, then L(ℝ) and V have exactly the same sets of reals and for any set of ordinals X with |X| ≥ΘL (ℝ), there is a Y∈L(ℝ) such that X⊆Y and |X| = |Y|. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 29 October 1999 / Published online: 12 December 2001
Rights and permissions
About this article
Cite this article
Cunningham, D. A covering lemma for L(ℝ). Arch. Math. Logic 41, 49–54 (2002). https://doi.org/10.1007/s001530200003
Issue Date:
DOI: https://doi.org/10.1007/s001530200003