Bases and Borel selectors for tall families

Kód výsledku v 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>
Výsledek na webu
<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>

Jazyk výsledku
angličtina
Název v původním jazyce
Bases and Borel selectors for tall families
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Bases and Borel selectors for tall families
Popis výsledku anglicky
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.

Projekt
<a href="/cs/project/GF15-34700L" target="_blank" >GF15-34700L: Kontinuum, forcing a velké kardinály</a><br>
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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