Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T09:39:06.060Z Has data issue: false hasContentIssue false
  • English
  • Français

Sequential Order under PFA

Published online by Cambridge University Press:  20 November 2018

Alan Dow
Alan Dow*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A.e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that it follows from PFA that there is no compact scattered space of height greater than $\omega $ in which the sequential order and the scattering heights coincide.

Keywords

54D5503E0503E3554A20sequential orderscattered spacesPFA
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 270 - 276
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Balogh, Z. T., On compact Hausdorff spaces of countable tightness. Proc. Amer. Math. Soc. 105(1989), no. 3, 755–764.Google Scholar
[2] Baškirov, A. I., The classification of quotient maps and sequential bicompacta. (Russian) Dokl. Akad. Nauk SSSR 217(1974), 745–748.Google Scholar
[3] Dow, A., Sequential order under MA, Topology Appl. 146/147(2005), 501–510. doi:10.1016/j.topol.2003.09.012Google Scholar
[4] Roitman, J., Superatomic Boolean algebras. In: Handbook of Boolean algebras, 3, North-Holland, Amsterdam, 1989, pp. 719–740.Google Scholar
[5] Shakhmatov, D. B., Compact spaces and their generalizations. In: Recent progress in general topology (Prague, 1991), North-Holland, Amsterdam, 1992, pp. 571–640.Google Scholar
[6] Shelah, S., Proper and improper forcing. Second ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998.Google Scholar
[7] Todorčević, S., A note on the proper forcing axiom. Axiomatic set theory (Boulder, Colo., 1983), Contemp. Math., 31, American Mathematical Society, Providence, RI, 1984, pp. 209–218.Google Scholar
[8] Vaughan, J. E., Small uncountable cardinals and topology. In: Open problems in topology, North-Holland, Amsterdam, 1990, pp. 195–218.Google Scholar