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IDEAL INDEPENDENT FAMILIES AND THE ULTRAFILTER NUMBER

Part of: Set theory

Published online by Cambridge University Press:  08 January 2021

JONATHAN CANCINO ,
OSVALDO GUZMÁN  and
ARNOLD W. MILLER
JONATHAN CANCINO
Affiliation:
CENTRO DE CIENCIAS MATEMÁTICAS UNAMMEXICO CITY, MEXICOE-mail: jcancino@matmor.unam.mxE-mail: oguzman@matmor.unam.mx
OSVALDO GUZMÁN
Affiliation:
CENTRO DE CIENCIAS MATEMÁTICAS UNAMMEXICO CITY, MEXICOE-mail: jcancino@matmor.unam.mxE-mail: oguzman@matmor.unam.mx
ARNOLD W. MILLER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN-MADISONMADISON, WI, USAE-mail: miller@math.wisc.edu
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Abstract

We say that $\mathcal {I}$ is an ideal independent family if no element of ${\mathcal {I}}$ is a subset mod finite of a union of finitely many other elements of ${\mathcal {I}}.$ We will show that the minimum size of a maximal ideal independent family is consistently bigger than both $\mathfrak {d}$ and $\mathfrak {u},$ this answers a question of Donald Monk.

Keywords

ideal independent familiesultrafiltersindpendent families

MSC classification

Primary: 03E17: Cardinal characteristics of the continuum
Secondary: 03E35: Consistency and independence results 03E05: Other combinatorial set theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 128 - 136
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Copyright
© The Association for Symbolic Logic 2021

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Footnotes

The first author was supported by CONACyT, scholarship 209499 and the second author gratefully acknowledge support from CONACyT grant A1-S-16164 and a PAPIIT grant IN 104220.

References

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