Hostname: page-component-59f8fd8595-9z55p Total loading time: 0 Render date: 2023-03-22T20:26:55.480Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true
  • English

Dual Borel Conjecture and Cohen reals

Published online by Cambridge University Press:  12 March 2014

Tomek Bartoszynski  and
Saharon Shelah
Tomek Bartoszynski
Affiliation:
National Science Foundation, Division of Mathematical Sciences, Arlington, Virginia 22230, USA. E-mail: tbartosz@nsf.gov, URL: http://tomek.bartoszynski.googlepages.com
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel. E-mail: shelah@math.huji.ac.il, URL: http://math.rutgers.edu/~shelah/
Get access Rights & Permissions[Opens in a new window]

Abstract

We construct a model of ZFC satisfying the Dual Borel Conjecture in which there is a set of size ℵ1 that does not have measure zero.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1293 - 1310
Copyright
Copyright © Association for Symbolic Logic 2010

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

[1]Bartoszynski, Tomek and Judah, Haim, Set Theory: on the structure of the real line, A. K. Peters, 1995.Google Scholar
[2]Carlson, Timothy J., Strong measure zero and strongly meager sets, Proceedings of the American Mathematical Society, vol. 118 (1993), no. 2, pp. 577–586.CrossRefGoogle Scholar
[3]Judah, Haim and Shelah, Saharon, MA(σ-centered): Cohen reals, strong measure zero sets and strongly meager sets, Israel Journal of Mathematics, vol. 68 (1989), no. 1, pp. 1–17.CrossRefGoogle Scholar
[4]Judah, Haim, Shelah, Saharon, and Woodin, W. H., The Borel conjecture, Annals of Pure and Applied Logic, vol. 50 (1990), no. 3, pp. 255–269.CrossRefGoogle Scholar
[5]Laver, Richard, On the consistency of Borel's conjecture, Acta Mathematica, vol. 137 (1976), no. 3-4, pp. 151–169.CrossRefGoogle Scholar
[6]Lorentz, G., On a problem of additive number theory, Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 838–841.CrossRefGoogle Scholar
[7]Pawlikowski, Janusz, Finite support iteration and strong measure zero sets, this Journal, vol. 55 (1990), no. 2, pp. 674–677.Google Scholar
[8]Rosłanowski, Andrzej and Shelah, Saharon, Norms on possibilities I: forcing with trees and creatures, Memoirs of the American Mathematical Society, American Mathematical Society, 1999.Google Scholar
[9]Shelah, Saharon, Proper and improper forcing, Perspectives in Logic, Springer-Verlag, 1998.CrossRefGoogle Scholar
[10]Shelah, Saharon, Non-Cohen oracle c.c.c., Journal of Applied Analysis, vol. 12 (2006), pp. 1–17.CrossRefGoogle Scholar