Martin's axiom is consistent with the existence of nowhere trivial automorphisms. Shelah, S. and Steprans, J. Proceedings of the American Mathematical Society, 130:2097–2106, 2002. arxiv:math/0011166
bibtex   
@article{ShSr:735,
author = {Shelah, Saharon and Steprans, Juris},
trueauthor = {Shelah, Saharon and Stepr\={a}ns, Juris},
fromwhere = {IL, 2},
journal = {Proceedings of the American Mathematical Society},
note = { arxiv:math/0011166 },
pages = {2097--2106},
title = {{Martin's axiom is consistent with the existence of
 nowhere	trivial automorphisms}},
volume = {130},
year = {2002},
}
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