When does the Katětov order imply that one ideal extends the other?

• Autorzy: Paweł Barbarski , Rafał Filipów , Nikodem Mrożek , Piotr Szuca
• Języki publikacji: EN

Abstrakty

EN

We consider the Katětov order between ideals of subsets of natural numbers ("$≤_{K}$") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals 𝓘 for which
$𝓘 ≤_{K} 𝒥 ⇒ 𝓘 ⊑ 𝒥$
for every ideal 𝒥. We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E15: Descriptive set theory
• 40A35: Ideal and statistical convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 130
• Numer: 1
• Strony: 91-102

Daty

wydano

2013

Twórcy

autor

Paweł Barbarski

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

Rafał Filipów

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

Nikodem Mrożek

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

Piotr Szuca

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/cm130-1-9