# On the ideal (v 0)

Open Mathematics (2008)

• Volume: 6, Issue: 2, page 218-227
• ISSN: 2391-5455

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## Abstract

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The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v 0) = ω 1 implies that (v 0) has the ideal type (c, ω 1, c).

## How to cite

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Piotr Kalemba, Szymon Plewik, and Anna Wojciechowska. "On the ideal (v 0)." Open Mathematics 6.2 (2008): 218-227. <http://eudml.org/doc/269328>.

@article{PiotrKalemba2008,
abstract = {The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min\{cf(c), r\}. The hypothesis cov(v 0) = ω 1 implies that (v 0) has the ideal type (c, ω 1, c).},
author = {Piotr Kalemba, Szymon Plewik, Anna Wojciechowska},
journal = {Open Mathematics},
keywords = {base v-matrix; doughnut; ideal type; ideal (v 0); base matrix},
language = {eng},
number = {2},
pages = {218-227},
title = {On the ideal (v 0)},
url = {http://eudml.org/doc/269328},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Piotr Kalemba
AU - Szymon Plewik
AU - Anna Wojciechowska
TI - On the ideal (v 0)
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 218
EP - 227
AB - The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v 0) = ω 1 implies that (v 0) has the ideal type (c, ω 1, c).
LA - eng
KW - base v-matrix; doughnut; ideal type; ideal (v 0); base matrix
UR - http://eudml.org/doc/269328
ER -

## References

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