Notre Dame Journal of Formal Logic

A Diamond Principle Consistent with AD

Daniel Cunningham

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We present a diamond principle R concerning all subsets of Θ, the supremum of the ordinals that are the surjective image of R. We prove that R holds in Steel’s core model K(R), a canonical inner model for determinacy.

Article information

Notre Dame J. Formal Logic, Volume 58, Number 3 (2017), 397-407.

Received: 19 June 2012
Accepted: 5 January 2015
First available in Project Euclid: 21 April 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

diamond principles determinacy Steel’s core model $\mathbf{K}(\mathbb{R})$


Cunningham, Daniel. A Diamond Principle Consistent with AD. Notre Dame J. Formal Logic 58 (2017), no. 3, 397--407. doi:10.1215/00294527-2017-0008.

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