Simple Cardinal Characteristics of the Continuum

Andreas Blass
1994 arXiv   pre-print
We classify many cardinal characteristics of the continuum according to the complexity, in the sense of descriptive set theory, of their definitions. The simplest characteristics (boldface Sigma^0_2 and, under suitable restrictions, Pi^0_2) are shown to have pleasant properties, related to Baire category. We construct models of set theory where (unrestricted) boldface Pi^0_2-characteristics behave quite chaotically and no new characteristics appear at higher complexity levels. We also discuss
more » ... me characteristics associated with partition theorems and we present, in an appendix, a simplified proof of Shelah's theorem that the dominating number is less than or equal to the independence number.
arXiv:math/9405202v1 fatcat:yes2yedjkfdelg6rf5josfqoiy