ON AUTOMORPHISMS OF P(λ)/[λ]<λ

J.A.K.O.B. Kellner, S. Shelah, A.R. TĂnasie

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the statement "all automorphisms of $\mathcal P(\lambda)/[\lambda]^{\lt \lambda}$ are trivial using set theory. We first show that MA imples the statement for regular uncountable cardinals $\lamba < 2^{\aleph_0}$ and the statement is false for measurable $\lambda$ if $2^\lamba =\lambda^{+}$. Then we construct a creature forcing to show that for "densly trivial", the statement can be forced for inaccesible cardinals $\lambda$ (together with $2^{\lambda}=\lambda^{++}$
Original languageEnglish
JournalJournal of Symbolic Logic
DOIs
Publication statusPublished - 2024

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