Keeping the covering number of the null ideal small
Fundamenta Mathematicae (2015)
- Volume: 231, Issue: 2, page 139-159
- ISSN: 0016-2736
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topTeruyuki Yorioka. "Keeping the covering number of the null ideal small." Fundamenta Mathematicae 231.2 (2015): 139-159. <http://eudml.org/doc/283170>.
@article{TeruyukiYorioka2015,
abstract = {It is proved that ideal-based forcings with the side condition method of Todorcevic (1984) add no random reals. By applying Judah-Repický's preservation theorem, it is consistent with the covering number of the null ideal being ℵ₁ that there are no S-spaces, every poset of uniform density ℵ₁ adds ℵ₁ Cohen reals, there are only five cofinal types of directed posets of size ℵ₁, and so on. This extends the previous work of Zapletal (2004).},
author = {Teruyuki Yorioka},
journal = {Fundamenta Mathematicae},
keywords = {side condition method; random reals},
language = {eng},
number = {2},
pages = {139-159},
title = {Keeping the covering number of the null ideal small},
url = {http://eudml.org/doc/283170},
volume = {231},
year = {2015},
}
TY - JOUR
AU - Teruyuki Yorioka
TI - Keeping the covering number of the null ideal small
JO - Fundamenta Mathematicae
PY - 2015
VL - 231
IS - 2
SP - 139
EP - 159
AB - It is proved that ideal-based forcings with the side condition method of Todorcevic (1984) add no random reals. By applying Judah-Repický's preservation theorem, it is consistent with the covering number of the null ideal being ℵ₁ that there are no S-spaces, every poset of uniform density ℵ₁ adds ℵ₁ Cohen reals, there are only five cofinal types of directed posets of size ℵ₁, and so on. This extends the previous work of Zapletal (2004).
LA - eng
KW - side condition method; random reals
UR - http://eudml.org/doc/283170
ER -
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