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

Tom 130 / 2013

Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca Colloquium Mathematicum 130 (2013), 91-102 MSC: Primary 03E05; Secondary 03E15, 40A35. DOI: 10.4064/cm130-1-9

Streszczenie

We consider the Katětov order between ideals of subsets of natural numbers (“$\leq_{K}$”) and its stronger variant—containing an isomorphic ideal (“$\sqsubseteq$”). In particular, we are interested in ideals $\mathcal{I}$ for which $$ \mathcal{I}\leq_{K}\mathcal{J}\ \Rightarrow\ \mathcal{I}\sqsubseteq\mathcal{J} $$ for every ideal $\mathcal{J}$. 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 “$\sqsubseteq$” (and vice versa).

Autorzy

  • Paweł BarbarskiInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail
  • Rafał FilipówInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail
  • Nikodem MrożekInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail
  • Piotr SzucaInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek