Strongly almost disjoint sets and weakly uniform bases

Z. T. Balogh; S. W. Davis; W. Just; Saharon Shelah; P. J. Szeptycki

doi:10.1090/s0002-9947-00-02599-x

Strongly almost disjoint sets and weakly uniform bases

Z. T. Balogh^*
, S. W. Davis
, W. Just
, Saharon Shelah
, P. J. Szeptycki

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of □_λ for singular A is proved. CECA is used to show that certain "almost point-< τ" families can be refined to point-< T families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of "every first countable Ti-space with a weakly uniform base has a point-countable base."

Original language	English
Pages (from-to)	4971-4987
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	352
Issue number	11
DOIs	https://doi.org/10.1090/s0002-9947-00-02599-x
State	Published - 2000
Externally published	Yes

Keywords

GCH, D
Point countable base
Strongly almost disjoint families
Weakly uniform base

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10.1090/s0002-9947-00-02599-x

Cite this

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keywords = "GCH, D, Point countable base, Strongly almost disjoint families, Weakly uniform base",

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AU - Balogh, Z. T.

AU - Davis, S. W.

AU - Just, W.

AU - Shelah, Saharon

AU - Szeptycki, P. J.

PY - 2000

Y1 - 2000

N2 - A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of □λ for singular A is proved. CECA is used to show that certain "almost point-< τ" families can be refined to point-< T families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of "every first countable Ti-space with a weakly uniform base has a point-countable base."

AB - A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of □λ for singular A is proved. CECA is used to show that certain "almost point-< τ" families can be refined to point-< T families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of "every first countable Ti-space with a weakly uniform base has a point-countable base."

KW - GCH, D

KW - Point countable base

KW - Strongly almost disjoint families

KW - Weakly uniform base

UR - https://www.scopus.com/pages/publications/23044524782

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

ER -

Strongly almost disjoint sets and weakly uniform bases

Abstract

Keywords

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