Superduper Properties - Hart, Joan; Kunen, Kenneth (Topology Proceedings, 2022)
The paper "Super Properties and Net Weight" [Topology Appl. 274 (2020)] discussed the property suHG (super HG) and showed that it is consistent with MA(N_1) to have a suHG space of uncount able net weight. Here, we introduce the superduper properties and show that sudu HG (superduper HG) is equivalent to countable net weight. As with the super varieties of the familiar HG, HS, HL, and HC properties, the suduHG, suduHS, and suduHL properties are all equivalent, while the property suduHC is strictly weaker than sudu HG. We shall also discuss two-parameter and three-parameter versions of these notions.