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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On strongly summable ultrafilters and union ultrafilters


Authors: Andreas Blass and Neil Hindman
Journal: Trans. Amer. Math. Soc. 304 (1987), 83-97
MSC: Primary 03E05; Secondary 03E35, 03E50
DOI: https://doi.org/10.1090/S0002-9947-1987-0906807-4
MathSciNet review: 906807
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Abstract: We prove that union ultrafilters are essentially the same as strongly summable ultrafilters but ordered-union ultrafilters are not. We also prove that the existence of ultrafilters of these sorts implies the existence of $ P$-points and therefore cannot be established in ZFC.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0906807-4
Article copyright: © Copyright 1987 American Mathematical Society