Four cardinals and their relations in ZF

Lorenz Halbeisen; Riccardo Plati; Salome Schumacher; Saharon Shelah

doi:10.1016/j.apal.2022.103200

Four cardinals and their relations in ZF

Lorenz Halbeisen^*
, Riccardo Plati
, Salome Schumacher
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

For a set M, fin(M) denotes the set of all finite subsets of M, M² denotes the Cartesian product M×M, [M]² denotes the set of all 2-element subsets of M, and seq^1-1(M) denotes the set of all finite sequences without repetition which can be formed with elements of M. Furthermore, for a set S, let |S| denote the cardinality of S. Under the assumption that the four cardinalities |[M]²|, |M²|, |fin(M)|, |seq^1-1(M)| are pairwise distinct and pairwise comparable in ZF, there are six possible linear orderings between these four cardinalities. We show that at least five of the six possible linear orderings are consistent with ZF.

Original language	English
Article number	103200
Journal	Annals of Pure and Applied Logic
Volume	174
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2022.103200
State	Published - Feb 2023

Bibliographical note

Publisher Copyright:
© 2022 The Author(s)

Keywords

Cardinals in ZF
Consistency results
Permutation models

Access to Document

10.1016/j.apal.2022.103200

Cite this

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AU - Halbeisen, Lorenz

AU - Plati, Riccardo

AU - Schumacher, Salome

AU - Shelah, Saharon

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KW - Permutation models

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ER -

Four cardinals and their relations in ZF

Abstract

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Keywords

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