Notre Dame Journal of Formal Logic

A Covering Lemma for HOD of K(ℝ)

Daniel W. Cunningham

Abstract

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 51, Number 4 (2010), 427-442.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1285765797

Digital Object Identifier
doi:10.1215/00294527-2010-027

Mathematical Reviews number (MathSciNet)
MR2741835

Zentralblatt MATH identifier
1217.03030

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]
Secondary: 03E45: Inner models, including constructibility, ordinal definability, and core models 03E60: Determinacy principles

Keywords
descriptive set theory determinacy fine structure

Citation

Cunningham, Daniel W. A Covering Lemma for HOD of K (ℝ). Notre Dame J. Formal Logic 51 (2010), no. 4, 427--442. doi:10.1215/00294527-2010-027. https://projecteuclid.org/euclid.ndjfl/1285765797


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References

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