## Simple Cardinal Characteristics Of The Continuum (1993)

Venue: | 63–90, Israel Math. Conf. Proc., 6, Bar-Ilan Univ., Ramat |

Citations: | 13 - 1 self |

### BibTeX

@INPROCEEDINGS{Blass93simplecardinal,

author = {Andreas Blass},

title = {Simple Cardinal Characteristics Of The Continuum},

booktitle = {63–90, Israel Math. Conf. Proc., 6, Bar-Ilan Univ., Ramat},

year = {1993},

pages = {63--90}

}

### OpenURL

### Abstract

. 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 (\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) \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. 1. Introduction Cardinal characteristics of the continuum are cardinal numbers, usually between @ 1 and c = 2 @0 inclusive, that give information about the real line R or the closely related sets P(!) (the power set of the set ! of natural numbers), [!] ! (the set of infinite subsets of !...