## Notre Dame Journal of Formal Logic

### Bounds on the Strength of Ordinal Definable Determinacy in Small Admissible Sets

Diego Rojas-Rebolledo

#### Abstract

We give upper and lower bounds for the strength of ordinal definable determinacy in a small admissible set. The upper bound is roughly a premouse with a measurable cardinal $\kappa$ of Mitchell order $\kappa^{++}$ and $\omega$ successors. The lower bound are models of ZFC with sequences of measurable cardinals, extending the work of Lewis, below a regular limit of measurable cardinals.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 53, Number 3 (2012), 351-371.

Dates
First available in Project Euclid: 24 September 2012

https://projecteuclid.org/euclid.ndjfl/1348524116

Digital Object Identifier
doi:10.1215/00294527-1716766

Mathematical Reviews number (MathSciNet)
MR2981013

Zentralblatt MATH identifier
1269.03052

#### Citation

Rojas-Rebolledo, Diego. Bounds on the Strength of Ordinal Definable Determinacy in Small Admissible Sets. Notre Dame J. Formal Logic 53 (2012), no. 3, 351--371. doi:10.1215/00294527-1716766. https://projecteuclid.org/euclid.ndjfl/1348524116

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