Borel Tukey morphisms and combinatorial cardinal invariants of the continuum

• Autorzy: Samuel Coskey , Tamás Mátrai , Juris Steprāns
• Języki publikacji: EN

Abstrakty

EN

We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality 𝔭 ≤ 𝔟 does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting and splitting numbers. Lastly, we use our results to give an embedding from the inclusion ordering on 𝒫(ω) into the Borel Tukey ordering on cardinal invariants.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 1
• Strony: 29-48

Daty

wydano

2013

Twórcy

autor

Samuel Coskey

• Department of Mathematics, Boise State University, 1910 University Dr., Boise, ID 83725-1555, U.S.A., Formerly at York University, Toronto, Canada

autor

Tamás Mátrai

• Alfréd Rényi Matematikai Kutatóintézet, Magyar Tudományos Akadémia, 13-15 Reáltanoda utca, H-1053 Budapest, Hungary

autor

Juris Steprāns

• Department of Mathematics and Statistics, N520 Ross, York University, 4700 Keele St., Toronto, ON, M3J 1P3, Canada

Identyfikatory

DOI

10.4064/fm223-1-2