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On well-splitting posets
ID
Repovš, Dušan
(
Author
),
ID
Zdomskyy, Lyubomyr
(
Author
)
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MD5: 1749D2BC1B9FE1051D07778520A3620A
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https://link.springer.com/article/10.1007/s00153-022-00818-6
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Abstract
We introduce a class of proper posets which is preserved under countable support iterations, includes ▫$\omega^\omega$▫-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.
Language:
English
Keywords:
splitting
,
bounding
,
Miller forcing
,
filter
,
Hurewicz space
,
mad family
,
Roitman problem
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Author Accepted Manuscript
Year:
2022
Number of pages:
Str. 995-1005
Numbering:
Vol. 61, iss. 7-8
PID:
20.500.12556/RUL-142141
UDC:
510.327:515.122
ISSN on article:
0933-5846
DOI:
10.1007/s00153-022-00818-6
COBISS.SI-ID:
101041411
Publication date in RUL:
21.10.2022
Views:
621
Downloads:
64
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Record is a part of a journal
Title:
Archive for mathematical logic
Shortened title:
Arch. math. log.
Publisher:
Springer
ISSN:
0933-5846
COBISS.SI-ID:
3165967
Projects
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0292
Name:
Topologija in njena uporaba
Funder:
ARRS - Slovenian Research Agency
Project number:
N1-0114
Name:
Algebrajski odtisi geometrijskih značilnosti v homologiji
Funder:
ARRS - Slovenian Research Agency
Project number:
N1-0083
Name:
Forsing, fuzija in kombinatorika odprtih pokritij
Funder:
FWF - Austrian Science Fund
Project number:
I2374-N35
Funder:
FWF - Austrian Science Fund
Project number:
I3709-N35
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