Filters, ideal independence and ideal Mrówka spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00637584" target="_blank" >RIV/67985840:_____/25:00637584 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/tran/9450" target="_blank" >https://doi.org/10.1090/tran/9450</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/9450" target="_blank" >10.1090/tran/9450</a>
Alternative languages
Result language
angličtina
Original language name
Filters, ideal independence and ideal Mrówka spaces
Original language description
A family A ⊆ [ω]ω such that for all finite {Xi}i∈n ⊆ A and A ∈ A{Xi}i∈n, the set AUi∈n Xi is infinite, is said to be ideal independent. We prove that an ideal independent family A is maximal if and only if A is J-completely separable and maximal J-almost disjoint for a particular ideal J on ω. We show that u ≤ smm, where smm is the minimal cardinality of maximal ideal independent family. This, in particular, establishes the independence of smm and i. Given an arbitrary set C of uncountable cardinals, we show how to simultaneously adjoin via forcing maximal ideal independent families of cardinality λ for each λ ∈ C, thus establishing the consistency of C ⊆ spec(smm). Assuming CH, we construct a maximal ideal independent family, which remains maximal after forcing with any proper, ωω-bounding, p-point preserving forcing notion and evaluate smm in several well-studied forcing extensions. We also study natural filters associated with ideal independence and introduce an analog of Mrówka spaces for ideal independent families.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
American Mathematical Society. Transactions
ISSN
0002-9947
e-ISSN
1088-6850
Volume of the periodical
378
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
5423-5439
UT code for WoS article
001544345000007
EID of the result in the Scopus database
2-s2.0-105010104737