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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Combinatorial set theory and cardinal function inequalities


Author: R. E. Hodel
Journal: Proc. Amer. Math. Soc. 111 (1991), 567-575
MSC: Primary 54A25; Secondary 04A20
MathSciNet review: 1039531
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Abstract: Three theorems of combinatorial set theory are proven. From the first we obtain the de Groot inequality $ \left\vert X \right\vert \leq {2^{hL(X)}}$, the Ginsburg-Woods inequality $ \left\vert X \right\vert \leq {2^{e(X)\Delta (X)}}$, the Erdös-Rado Partition Theorem for $ n = 2$, and set-theoretic versions of the Hajnal-Juhász inequalities $ \left\vert X \right\vert \leq {2^{c(X)\chi (X)}}$ and $ \left\vert X \right\vert \leq {2^{s(X)\psi (X)}}$. From the second we obtain a generalization of the Arhangel'skiĭ inequality $ \left\vert X \right\vert \leq {2^{L(X)\chi (X)}}$. From the third we obtain the Charlesworth inequality $ n(X) \leq psw{(X)^{L(X)}}$ and a generalization of the Burke-Hodel inequality $ \left\vert {K(X)} \right\vert \leq {2^{e(X)psw(X)}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1039531-7
PII: S 0002-9939(1991)1039531-7
Keywords: Lindelöf degree, extent, separating cover, Erdös-Rado Partition Theorem, cardinal functions
Article copyright: © Copyright 1991 American Mathematical Society