## Strongly almost disjoint sets and weakly uniform bases

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- by Z. T. Balogh, S. W. Davis, W. Just, S. Shelah and P. J. Szeptycki PDF
- Trans. Amer. Math. Soc.
**352**(2000), 4971-4987 Request permission

## Abstract:

A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of $\Box _\lambda$ for singular $\lambda$ is proved. CECA is used to show that certain “almost point-$<\tau$” families can be refined to point-$< \tau$ 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 $T_1$-space with a weakly uniform base has a point-countable base.”## References

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## Additional Information

**Z. T. Balogh**- Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
- Email: ztbalogh@miavx1.acs.muohio.edu
**S. W. Davis**- Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
- Email: swdavis@miavx1.muohio.edu
**W. Just**- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- Email: just@math.ohiou.edu
**S. Shelah**- Affiliation: Institute of Mathematics, The Hebrew University, Givat Ram, 91904 Jerusalem, Israel
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
**P. J. Szeptycki**- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- Email: szeptyck@math.ohiou.edu
- Received by editor(s): March 17, 1998
- Published electronically: June 20, 2000
- Additional Notes: The first author’s research was partially supported by NSF grant DMS-9623391. The third author’s research was done during visits at Rutgers University and The Hebrew University, Jerusalem, which were supported by NSF grant DMS-9704477 and the Landau Center. The fourth author was partially supported by the Israel Basic Research Fund. This is publication number 674 in Shelah’s publication list.
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 4971-4987 - MSC (2000): Primary 03E05, 03E35, 03E75, 54D70
- DOI: https://doi.org/10.1090/S0002-9947-00-02599-X
- MathSciNet review: 1707497