The mouse set conjecture for sets of reals

Grigor Sargsyan; John Steel

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arXiv · 2110.06083

The mouse set conjecture for sets of reals

Grigor Sargsyan·John Steel

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Abstract

Recall that the Mouse Set Conjecture says that under AD++V=L(P(R)), a real is ordinal definable if and only if it belongs to an iterable mouse. The Mouse Set Conjecture for sets of reals says that under the same theory, a set of reals is ordinal definable from a real if and only if it belongs to a mouse over the reals. We prove that the Mouse Set Conjecture implies the Mouse Set Conjecture for sets of reals.

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BibTeX RIS

Grigor Sargsyan, John Steel. 2021-10-12. The mouse set conjecture for sets of reals. https://arxiv.org/abs/2110.06083

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