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ON AUTOMORPHISMS OF
${\mathcal {P}}(\lambda )/[\lambda ]^{<\lambda }$
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 89 / Issue 4 / December 2024
- Published online by Cambridge University Press:
- 16 May 2024, pp. 1476-1512
- Print publication:
- December 2024
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- Article
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We investigate the statement “all automorphisms of
${\mathcal {P}}(\lambda )/[\lambda ]^{<\lambda }$ are trivial.” We show that MA implies the statement for regular uncountable 
$\lambda <2^{\aleph _0}$, that the statement is false for measurable 
$\lambda $ if 
$2^\lambda =\lambda ^+$, and that for “densely trivial” it can be forced (together with 
$2^\lambda =\lambda ^{++}$) for inaccessible 
$\lambda $.
