Some Applications of the Katětov Order on Borel Ideals

• Autorzy: Mrożek, N.
• Języki publikacji: EN

Abstrakty

EN

We construct an embedding of the algebra P(ω)/Fin into the family of summable ideals with the Katětov order. This construction will be used to solve two problems: about the relation between the Katětov order and the ideal Baire classes of functions, and about long chains of ideals alternately with and without the property of being a P-ideal.

Słowa kluczowe

EN

Katětov order; P-ideal; Baire classes; summable ideal

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2016
• Tom: Vol. 64, no. 1
• Strony: 21--28
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Mrożek, N.

• Institute of Mathematics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk,, Poland,

Bibliografia

• [1] P. Barbarski, R. Filipów, N. Mrożek, and P. Szuca, When does the Katětov order imply that one ideal extends the other?, Colloq. Math. 130 (2013), 91–102.
• [2] O. Guzmán-González and D. Meza-Alcántara, Some structural aspects of the Katětov order on Borel ideals, Order, to appear.
• [3] M. Hrušák and S. García Ferreira, Ordering MAD families à la Katětov, J. Symbolic Logic 68 (2003), 1337–1353.
• [4] M. Katětov, Products of filters, Comment. Math. Univ. Carolin. 9 (1968), 173–189.
• [5] M. Katětov, On descriptive classes of functions, in: Theory of Sets and Topology (in honour of Felix Hausdorff, 1868–1942), Deutsch. Verlag Wiss., Berlin, 1972, 265–278.
• [6] P. Kostyrko, T. Šalát, and W. Wilczyński, I-convergence, Real Anal. Exchange 26 (2000/01), 669–685.
• [7] A. Kwela, A note on a new ideal, J. Math. Anal. Appl. 430 (2015), 932–949.
• [8] M. Laczkovich and I. Recław, Ideal limits of sequences of continuous functions, Fund. Math. 203 (2009), 39–46.
• [9] A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), 59–111.
• [10] D. Meza-Alcántara, Ideals and filters on a countable set, Ph.D. thesis, Univ. Nacional Autónoma de México, 2009.
• [11] S. Solecki, Analytic ideals and their applications, Ann. Pure Appl. Logic 99 (1999), 51–72.
• [12] S. Solecki, Filters and sequences, Fund. Math. 163 (2000), 215–228.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

Identyfikatory

DOI

10.4064/ba8055-6-2016