The forcing construction ℛmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.
"The nonstationary ideal in the ℛmax extension." J. Symbolic Logic 72 (1) 138 - 158, March 2007. https://doi.org/10.2178/jsl/1174668389