2021/10/12 by Grigor Sargsyan, Sargsyan, Grigor, John Steel +2
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO
paper · pdf · doi:10.48550/arxiv.2110.06083
arxiv created 2021/10/12 · openalex publication_date 2021/10/12 · arxiv updated 2021/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.