English

The mouse set conjecture for sets of reals

Logic 2021-10-13 v1

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.

Keywords

Cite

@article{arxiv.2110.06083,
  title  = {The mouse set conjecture for sets of reals},
  author = {Grigor Sargsyan and John Steel},
  journal= {arXiv preprint arXiv:2110.06083},
  year   = {2021}
}