# Sh:848

• Mildenberger, H., & Shelah, S. (2009). Specializing Aronszajn trees and preserving some weak diamonds. J. Appl. Anal., 15(1), 47–78.
• Abstract:
We show that \diamondsuit({\mathbb R}, {\mathcal L}, \not\in) together with “all Aronszajn trees are special” is consistent relative to ZFC. The weak diamond for the uniformity of Lebegue null sets was the only weak diamond in the Cichoń diagramme for relations whose consistency together with “all Aronszajn trees are special” was not yet settled. We can have CH or 2^{\aleph_0} = \aleph_2. Our techniques give more on coverings by related small sets that are preserved in iterations that are stronger relatives to [Sh:f, Chap. V, sect. 5–7]
• Current version: 2008-09-08_11 (23p) published version (32p)
Bib entry
@article{Sh:848,
author = {Mildenberger, Heike and Shelah, Saharon},
title = {{Specializing Aronszajn trees and preserving some weak diamonds}},
journal = {J. Appl. Anal.},
fjournal = {Journal of Applied Analysis},
volume = {15},
number = {1},
year = {2009},
pages = {47--78},
issn = {1425-6908},
mrnumber = {2537976},
mrclass = {03E35 (03E15 03E17 03E50)},
doi = {10.1515/JAA.2009.47}
}