Transactions of the American Mathematical Society

Author(s): Z. T. Balogh; S. W. Davis; W. Just; S. Shelah; P. J. Szeptycki
Journal: Trans. Amer. Math. Soc. 352 (2000), 4971-4987.
MSC (2000): Primary 03E05, 03E35, 03E75, 54D70
Posted: June 20, 2000
Retrieve article in: PDF
This article is available free of charge

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

-space with a weakly uniform base has a point-countable base.''

1.: A. V. Arhangel'skii, W. Just, E. A. Reznichenko, and P. J. Szeptycki; Sharp bases and weakly uniform bases versus point-countable bases, to appear in Topology and its Applications.
2.: S. W. Davis, G. M. Reed, and M. L. Wage; Further results on weakly uniform bases, Houston Journal of Mathematics, 2 (1976) 57-63. MR 52:15365
3.: A. Hajnal, I. Juhász, and S. Shelah [HJSh249]; Splitting strongly almost disjoint families, TAMS 295 (1986) 369-387. MR 87i:03098
4.: R. W. Heath and W. F. Lindgren; Weakly uniform bases, Houston J. Math. 2 (1976) 85-90. MR 52:15364
5.: S. Shelah [Sh108]; On Successors of Singular Cardinals, in: Logic Colloquium 78 (M. Boffa, D. van Dalen, K. McAloon, eds.), 357-380, North-Holland 1979. MR 82d:03079
6.: S. Shelah [Sh88a]; Appendix: On stationary sets (to ``Classification of nonelementary classes II. Abstract elementary classes''), in: Classification Theory, Proceedings of the USA-Israel Conference on Classification Theory, Chicago, December 1985, J. T. Baldwin, ed., LNM 1292, 483-495, Springer 1987. MR 91h:03046
7.: S. Shelah [Sh420]; Advances in Cardinal Arithmetic, Finite and Infinite Combinatorics in Sets and Logic (N. W. Sauer et al. eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 411, Kluwer 1993, 355-383. MR 95h:03112

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03E05, 03E35, 03E75, 54D70

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
Email: shelah@math.huji.ac.il

P. J. Szeptycki
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: szeptyck@math.ohiou.edu

DOI: 10.1090/S0002-9947-00-02599-X
PII: S 0002-9947(00)02599-X
Keywords: GCH, $\Box$, strongly almost disjoint families, weakly uniform base, point countable base
Received by editor(s): March 17, 1998
Posted: 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 of article: Copyright 2000, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS