Universal sets for ideals

• Autorzy: Cieślak A. , Michalski M.

Identyfikatory

DOI

10.4064/ba8146-5-2018

• Języki publikacji: EN

Abstrakty

EN

We consider the notion of universal sets for ideals. We show that there exist universal sets of minimal Borel complexity for classical ideals like the null subsets of 2^ω and the meager subsets of any Polish space, and demonstrate that the existence of such sets is helpful in establishing some facts about the real line in generic extensions. We also construct universal sets for E, the σ-ideal generated by closed null subsets of 2^ω, and for some ideals connected with forcing notions: the K_σ subsets of ω^ω and the Laver ideal. We also consider Fubini products of ideals and show that there are Σ⁰₃ universal sets for N[symbol]M and M[symbol]N.

Słowa kluczowe

EN

universal set; ideal; Borel rank; Borel complexity; absolute; Fubini product; Polish space

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2018
• Tom: Vol. 66, no. 2
• Strony: 157--166
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Cieślak A.

• Department of Computer Science, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Michalski M.

• Department of Computer Science, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).