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
HTML articles powered by AMS MathViewer

by Saharon Shelah and Juris Steprāns PDF

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

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.

References

Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295
Saharon Shelah and J. Steprāns, Nontrivial homeomorphisms of $\beta \textbf {N}\sbs \textbf {N}$ without the continuum hypothesis, Fund. Math. 132 (1989), no. 2, 135–141. MR 1002627, DOI 10.4064/fm-132-2-135-141
Saharon Shelah and Juris Steprāns, Somewhere trivial autohomeomorphisms, J. London Math. Soc. (2) 49 (1994), no. 3, 569–580. MR 1271551, DOI 10.1112/jlms/49.3.569
Boban Veli ković, Definable automorphisms of ${\scr P}(\omega )/\textrm {fin}$, Proc. Amer. Math. Soc. 96 (1986), no. 1, 130–135. MR 813825, DOI 10.1090/S0002-9939-1986-0813825-8
Boban Veli ković, $\textrm {OCA}$ and automorphisms of ${\scr P}(\omega )/\textrm {fin}$, Topology Appl. 49 (1993), no. 1, 1–13. MR 1202874, DOI 10.1016/0166-8641(93)90127-Y