Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T07:12:28.321Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite support iteration and strong measure zero sets

Published online by Cambridge University Press:  12 March 2014

Janusz Pawlikowski
Janusz Pawlikowski*
Affiliation:
Institute of Mathematics, University of Wrocław, 50-384 Wrocław, Poland Department of Mathematics, University of Colorado, Boulder, Colorado 80309
Get access Rights & Permissions [Opens in a new window]

Abstract

Any finite support iteration of posets with precalibre ℵ1 which has the length of cofinahty greater than ω1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ1 strong measure zero sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 674 - 677
Copyright
Copyright © Association for Symbolic Logic 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[C] Carlson, T., Dual Borel conjecture (unpublished).Google Scholar
[GMS] Galvin, F., Mycielski, J. and Solovay, R. M., Strong measure zero sets, Notices of the American Mathematical Society, vol. 26 (1979), p. A–380.Google Scholar
[IS] Ihoda, J. I. and Shelah, S., MA(σ-centered): Cohen reals, strong measure zero sets and strongly meager sets (preprint).Google Scholar
[L] Lorentz, G. G., On a problem of additive number theory, Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 838–841.CrossRefGoogle Scholar
[M] Miller, A. W., Special subsets of the real line, Handbook of set-theoretic topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, Amsterdam, 1984, pp. 201–233.CrossRefGoogle Scholar
[T] Truss, J. K., Sets having calibre ℵ1, Logic colloquium '76 (Gandy, R. O. and Hyland, J. M. E., editors), North-Holland, Amsterdam, 1977, pp. 595–612.Google Scholar