## Notre Dame Journal of Formal Logic

### A Diamond Principle Consistent with AD

Daniel Cunningham

#### Abstract

We present a diamond principle $\lozenge_{\mathbb{R}}$ concerning all subsets of $\Theta$, the supremum of the ordinals that are the surjective image of $\mathbb{R}$. We prove that $\lozenge_{\mathbb{R}}$ holds in Steel’s core model $\mathbf{K}(\mathbb{R})$, a canonical inner model for determinacy.

#### Article information

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

Dates
Accepted: 5 January 2015
First available in Project Euclid: 21 April 2017

https://projecteuclid.org/euclid.ndjfl/1492761611

Digital Object Identifier
doi:10.1215/00294527-2017-0008

Mathematical Reviews number (MathSciNet)
MR3681101

Zentralblatt MATH identifier
06761615

#### Citation

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. https://projecteuclid.org/euclid.ndjfl/1492761611

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