On well-splitting posets

Abstract

We introduce a class of proper posets which is preserved under countable support iterations, includes ${\omega }^{\omega }$-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.

10 pages. This is the submitted version, but it is rather close to the accepted one

References in corpus (1)

• Mathias--Prikry and Laver type forcing; Summable ideals, coideals, and $+$-selective filters