Remarks on gaps in equation image



The structure equation image and gaps in analytic quotients of equation image have been studied in the literature 2, 3, 1. We prove that the structures equation image and equation image have gaps of type equation image, and there are no (λ, ω)-gaps for equation image, where equation image is the additivity number of the meager ideal. We also prove the existence of (ω1, ω1)-gaps in these structures. Finally we characterize the cofinality of the meager ideal equation image using families of sets in equation image.