  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 some 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.
