DOWNSETS AND GENERALIZED DESCRIPTIVE SET THEORY

Downsets over a regular cardinal κ arise from Π1 normal form. For inaccessible κ downsets correspond to the trees of generalized descriptive set theory. Basic properties of downsets, trees, and the correspondence are considered. A new characterization of weak compactness is given. Some facts about Σ1 WPS’s are proved. AMS Subject Classification: 03E55