Simple Cardinal Characteristics of the Continuum

Andreas Blass

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Simple Cardinal Characteristics of the Continuum

Andreas Blass

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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 (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.

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Andreas Blass. 1994-05-20. Simple Cardinal Characteristics of the Continuum. https://arxiv.org/abs/math/9405202

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