Halfway new cardinal characteristics

Jörg Brendle; Lorenz J. Halbeisen; Lukas Daniel Klausner; Marc Lischka; Saharon Shelah

doi:10.1016/j.apal.2023.103303

Halfway new cardinal characteristics

Jörg Brendle
, Lorenz J. Halbeisen
, Lukas Daniel Klausner^*
, Marc Lischka
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Based on the well-known cardinal characteristics s, r and i, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of [Formula presented], as well as several results about possible values of [Formula presented].

Original language	English
Article number	103303
Journal	Annals of Pure and Applied Logic
Volume	174
Issue number	9
DOIs	https://doi.org/10.1016/j.apal.2023.103303
State	Published - 1 Oct 2023

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Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

Cardinal characteristics of the continuum
Independence number
Reaping number
Splitting number

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10.1016/j.apal.2023.103303

Cite this

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AU - Halbeisen, Lorenz J.

AU - Klausner, Lukas Daniel

AU - Lischka, Marc

AU - Shelah, Saharon

PY - 2023/10/1

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N2 - Based on the well-known cardinal characteristics s, r and i, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of [Formula presented], as well as several results about possible values of [Formula presented].

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KW - Cardinal characteristics of the continuum

KW - Independence number

KW - Reaping number

KW - Splitting number

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Halfway new cardinal characteristics

Abstract

Bibliographical note

Keywords

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