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USUBA’S PRINCIPLE $\mathrm {UB}_\lambda $ CAN FAIL AT SINGULAR CARDINALS

Part of: Set theory

Published online by Cambridge University Press:  07 September 2023

MOHAMMAD GOLSHANI Open the ORCID record for MOHAMMAD GOLSHANI [Opens in a new window]  and
SAHARON SHELAH Open the ORCID record for SAHARON SHELAH [Opens in a new window]
MOHAMMAD GOLSHANI*
Affiliation:
SCHOOL OF MATHEMATICS INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM) P.O. BOX 19395-5746, TEHRAN IRAN
SAHARON SHELAH
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS THE HEBREW UNIVERSITY OF JERUSALEM, EDMOND J. SAFRA CAMPUS GIVAT RAM, JERUSALEM 91904 ISRAEL and DEPARTMENT OF MATHEMATICS, RUTGERS THE STATE UNIVERSITY OF NEW JERSEY, HILL CENTER—BUSCH CAMPUS 110 FRELINGHUYSEN ROAD, PISCATAWAY, NJ 08854-8019 USA E-mail: shelah@math.huji.ac.il URL: http://shelah.logic.at
*
E-mail: golshani.m@gmail.com
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Abstract

We answer a question of Usuba by showing that the combinatorial principle $\mathrm {UB}_\lambda $ can fail at a singular cardinal. Furthermore, $\lambda $ can be taken to be $\aleph _\omega .$

Keywords

Usuba’s questionsingular cardinalsChang’s conjecture

MSC classification

Primary: 03E05: Other combinatorial set theory 03E55: Large cardinals

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 1 , March 2024 , pp. 195 - 203
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

Eskew, M. and Hayut, Y., On the consistency of local and global versions of Chang’s conjecture . Transactions of the American Mathematical Society , vol. 370 (2018), no. 4, pp. 2879–2905. Erratum: Transactions of the American Mathematical Society, vol. 374 (2021), no. 1, p. 753.CrossRefGoogle Scholar
Hayut, Y., Magidor–Malitz reflection . Archive for Mathematical Logic , vol. 56 (2017), nos. 3–4, pp. 253–272.CrossRefGoogle Scholar
Levinski, J.-P., Magidor, M., and Shelah, S., Chang’s conjecture for ${\aleph}_{\omega }$ . Israel Journal of Mathematics , vol. 69 (1990), no. 2, pp. 161–172.CrossRefGoogle Scholar
Shelah, S., Non-reflection of the bad set for ${\check{I}}_{\theta}[\lambda]$ and pcf. Acta Mathematica Hungarica, vol. 141 (2013), nos. 1–2, pp. 11–35.CrossRefGoogle Scholar
Usuba, T., New combinatorial principle on singular cardinals and normal ideals . Mathematical Logic Quarterly , vol. 64 (2018), nos. 4–5, pp. 395–408.CrossRefGoogle Scholar