Rothberger gaps in fragmented ideals

• Autorzy: Jörg Brendle , Diego Alejandro Mejía
• Języki publikacji: EN

Abstrakty

EN

The Rothberger number 𝔟(ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra 𝓟(ω)/ℐ. We investigate 𝔟(ℐ) for a class of $F_{σ}$ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum many) different Rothberger numbers associated with fragmented ideals.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E05: Other combinatorial set theory
• 03E15: Descriptive set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 227
• Numer: 1
• Strony: 35-68

Daty

wydano

2014

Twórcy

autor

Jörg Brendle

• Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, 657-8501 Kobe, Japan

autor

Diego Alejandro Mejía

• Graduate School of System Informatics, Kobe University, Kobe, Japan

Identyfikatory

DOI

10.4064/fm227-1-4