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CICHOŃ’S MAXIMUM WITH EVASION NUMBER

Published online by Cambridge University Press:  27 January 2025

TAKASHI YAMAZOE
TAKASHI YAMAZOE*
Affiliation:
GRADUATE SCHOOL OF SYSTEM INFORMATICS KOBE UNIVERSITY, ROKKO–DAI 1–1 NADA–KU, 657–8501 KOBE JAPAN
*
E-mail: 212x502x@cloud.kobe-u.jp
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Abstract

We show that the evasion number $\mathfrak {e}$ can be added to Cichoń’s maximum with a distinct value. More specifically, it is consistent that $\aleph _1<\operatorname {\mathrm {add}}(\mathcal {N})<\operatorname {\mathrm {cov}}(\mathcal {N})<\mathfrak {b}<\mathfrak {e}<\operatorname {\mathrm {non}}(\mathcal {M})<\operatorname {\mathrm {cov}}(\mathcal {M})<\mathfrak {d}<\operatorname {\mathrm {non}}(\mathcal {N})<\operatorname {\mathrm {cof}}(\mathcal {N})<2^{\aleph _0}$ holds.

Keywords

cardinal invariantsCichoń’s maximumevasion numberultrafilter-limit
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 31
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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