Small-large subgroups of the reals

Andrzej Ros Lanowski; Saharon Shelah

doi:10.1515/ms-2017-0117

Small-large subgroups of the reals

Andrzej Ros Lanowski
, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non-meager Lebesgue null subgroup of ℝ, while it is consistent that there there is no non-null meager subgroup of ℝ.

Original language	English
Pages (from-to)	473-484
Number of pages	12
Journal	Mathematica Slovaca
Volume	68
Issue number	3
DOIs	https://doi.org/10.1515/ms-2017-0117
State	Published - 26 Jun 2018

Bibliographical note

Publisher Copyright:
© 2018 De Gruyter Open Ltd. All rights rserved.

Keywords

Borel hulls
additive subgroups of the reals
forcing
meager ideal
null ideal

Access to Document

10.1515/ms-2017-0117

Cite this

@article{3851843f52814904ae57008bb3ccb868,

title = "Small-large subgroups of the reals",

abstract = "We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non-meager Lebesgue null subgroup of ℝ, while it is consistent that there there is no non-null meager subgroup of ℝ.",

keywords = "Borel hulls, additive subgroups of the reals, forcing, meager ideal, null ideal",

author = "Lanowski, \{Andrzej Ros\} and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 2018 De Gruyter Open Ltd. All rights rserved.",

year = "2018",

month = jun,

day = "26",

doi = "10.1515/ms-2017-0117",

language = "אנגלית",

volume = "68",

pages = "473--484",

journal = "Mathematica Slovaca",

issn = "0139-9918",

publisher = "Walter de Gruyter GmbH",

number = "3",

}

TY - JOUR

T1 - Small-large subgroups of the reals

AU - Lanowski, Andrzej Ros

AU - Shelah, Saharon

PY - 2018/6/26

Y1 - 2018/6/26

N2 - We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non-meager Lebesgue null subgroup of ℝ, while it is consistent that there there is no non-null meager subgroup of ℝ.

AB - We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non-meager Lebesgue null subgroup of ℝ, while it is consistent that there there is no non-null meager subgroup of ℝ.

KW - Borel hulls

KW - additive subgroups of the reals

KW - forcing

KW - meager ideal

KW - null ideal

UR - https://www.scopus.com/pages/publications/85047861709

U2 - 10.1515/ms-2017-0117

DO - 10.1515/ms-2017-0117

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85047861709

SN - 0139-9918

VL - 68

SP - 473

EP - 484

JO - Mathematica Slovaca

JF - Mathematica Slovaca

IS - 3

ER -

Small-large subgroups of the reals

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this