Bases and Borel selectors for tall families

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00503652" target="_blank" >RIV/67985840:_____/19:00503652 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/jsl.2018.66" target="_blank" >http://dx.doi.org/10.1017/jsl.2018.66</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2018.66" target="_blank" >10.1017/jsl.2018.66</a>

Result language
angličtina
Original language name
Bases and Borel selectors for tall families
Original language description
Given a family of infinite subsets of N, we study when there is a Borel function S: 2N → 2 N such that for every infinite x insin, 2 N , S(X) ⊂ X and. We show that the family of homogeneous sets (with respect to a partition of a front) as given by the Nash-Williams' theorem admits such a Borel selector. However, we also show that the analogous result for Galvin's lemma is not true by proving that there is an Fσ tall ideal on N without a Borel selector. The proof is not constructive since it is based on complexity considerations. We construct a pi, 1 2 tall ideal on without a tall closed subset.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF15-34700L" target="_blank" >GF15-34700L: The continuum, forcing and large cardinals</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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