Martin’s Axiom is consistent with the existence of nowhere trivial automorphisms

Shelah, Saharon; Steprāns, Juris

doi:10.1090/S0002-9939-01-06280-3

Martin’s Axiom is consistent with the existence of nowhere trivial automorphisms
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by Saharon Shelah and Juris Steprāns

Proc. Amer. Math. Soc. 130 (2002), 2097-2106

DOI: https://doi.org/10.1090/S0002-9939-01-06280-3

Published electronically: December 27, 2001

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Abstract:

Martin’s Axiom does not imply that all automorphisms of ${\mathcal P}(\mathbb {N})/ [\mathbb {N}]^{<\aleph _0}$ are somewhere trivial. An alternate method for obtaining models where every automorphism of ${\mathcal P}(\mathbb {N})/[\mathbb {N}]^{<\aleph _0}$ is somewhere trivial is explained.

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