On automorphisms of \mathcal P(λ)/[λ]^<λ

2022/06/05 by Kellner, Jakob, Latif, Anda, Shelah, Saharon
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2206.02228

Abstract

We investigate the statement ``all automorphisms of \mathcal P(λ)/[λ]<sup>&lt;λ</sup> are trivial''. We show that MA implies the statement for regular uncountable λ&lt;2<sup>ℵ<sub>0</sub></sup>; that the statement is false for measurable λ if 2<sup>λ</sup>=λ<sup>+</sup>; and that for ``densely trivial'' it can be forced (together with 2^λ=λ⁺⁺) for inaccessible λ.

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