Ideals over Uncountable Sets: Application of Almost Disjoint Functions and Generic Ultrapowers: Application of Almost Disjoint Functions and Generic Ultrapowers

Couverture
American Mathematical Soc., 1979 - 71 pages
This work is a systematic study of ideals over uncountable sets. In particular, we investigate the role of various properties of ideals in arithmetic of cardinal numbers. We also study consequences of existence of precipitous ideals for the generalized continuum hypothesis and the singular cardinals problem.
 

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Table des matières

0 Introduction
1
1 Ideals over uncountable sets
6
2 Generic ultrapowers
16
3 Saturation of ideals and the GCH
30
4 The singular cardinals problem
45
5 Almost disjoint functions
54
6 Applications of almost disjoint functions
64
7 Nonregular ultrafilters and the GCH
67
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