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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Mathias forcing which does not add dominating reals


Author: R. Michael Canjar
Journal: Proc. Amer. Math. Soc. 104 (1988), 1239-1248
MSC: Primary 03E05; Secondary 03E35, 03E40, 04A20
DOI: https://doi.org/10.1090/S0002-9939-1988-0969054-2
MathSciNet review: 969054
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Abstract: Assume that there is no dominating family of reals of cardinality $ < c$. We show that there then exists an ultrafilter on the set of natural numbers such that its associated Mathias forcing does not adjoin any real which dominates all ground model reals. Such ultrafilters are necessarily $ P$-points with no $ Q$-points below them in the Rudin-Keisler order.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0969054-2
Article copyright: © Copyright 1988 American Mathematical Society