Towers in Filters, Cardinal Invariants and Luzin Type Families
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F18%3A10314909" target="_blank" >RIV/00216208:11210/18:10314909 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/abs/1605.04735" target="_blank" >https://arxiv.org/abs/1605.04735</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2017.52" target="_blank" >10.1017/jsl.2017.52</a>
Alternative languages
Result language
angličtina
Original language name
Towers in Filters, Cardinal Invariants and Luzin Type Families
Original language description
We investigate which filters on ω can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in ). We prove the following results: (1)Many classical examples of nice tall filters contain no towers (in ZFC). (2)It is consistent that tall analytic P-filters contain towers of arbitrary regular height (simultaneously for many regular cardinals as well). (3)It is consistent that all towers generate nonmeager filters (this answers a question of P. Borodulin-Nadzieja and D. Chodounský), in particular (consistently) Borel filters do not contain towers. (4)The statement "Every ultrafilter contains towers." is independent of ZFC (this improves an older result of K. Kunen, J. van Mill, and C. F. Mills). Furthermore, we study many possible logical (non)implications between the existence of towers in filters, inequalities between cardinal invariants of filters ( , , , and ), and the existence of Luzin type families (of size ), that is, if is a filter then is an -Luzin family if is countable for every .
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF17-33849L" target="_blank" >GF17-33849L: Filters, Ultrafilters and Connections with Forcing</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Symbolic Logic
ISSN
0022-4812
e-ISSN
—
Volume of the periodical
83
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
50
Pages from-to
1013-1062
UT code for WoS article
000448035800008
EID of the result in the Scopus database
2-s2.0-85055563014