← Back to Problems
Set Theory / Mathematical LogicResearchAI-Generated

Does the dominating number equaling omega_1 imply that the almost disjointness number also equals omega_1, and if so, can this implication be reversed or shown independent of ZFC?

Related: Cichon's diagram, Blass-Shelah theorem on cardinal characteristics, Malliaris-Shelah theorem on p equals t

Resolving whether a equals omega_1 implies d equals omega_1 would clarify a significant portion of the diagram of cardinal characteristics below the continuum. If the implication is one-directional only, it would refine our understanding of which combinatorial properties of the reals are truly distinct. If the two are equivalent under ZFC, it would suggest a deep structural connection between domination and almost disjointness that could illuminate further relations among characteristics like the bounding number b, the splitting number s, and the reaping number r. Such a result would likely require new forcing technology with fine-grained control over both families simultaneously.

View Source Paper →