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COMPACT CARDINALS AND EIGHT VALUES IN CICHOŃ’S DIAGRAM

Published online by Cambridge University Press:  01 August 2018

JAKOB KELLNER ,
ANDA RAMONA TĂNASIE  and
FABIO ELIO TONTI
JAKOB KELLNER
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TECHNISCHE UNIVERSITÄT WIEN (TU WIEN) WIEN, AUSTRIAE-mail:jakob.kellner@tuwien.ac.at
ANDA RAMONA TĂNASIE
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TECHNISCHE UNIVERSITÄT WIEN (TU WIEN) WIEN, AUSTRIAE-mail:anda-ramona.tanasie@tuwien.ac.at
FABIO ELIO TONTI
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TECHNISCHE UNIVERSITÄT WIEN (TU WIEN) WIEN, AUSTRIAE-mail:fabio.tonti@tuwien.ac.at
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Abstract

Assuming three strongly compact cardinals, it is consistent that

$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) < \mathfrakb < \mathfrakd < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$

Under the same assumption, it is consistent that

$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) < non\left( {\cal M} \right) < cov\left( {\cal M} \right) < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$

Keywords

03E17set theory of the realsCichoń’s diagramlarge continuumlarge cardinals
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 790 - 803
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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