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A COUNTABLE STRUCTURE DOES NOT HAVE A FREE UNCOUNTABLE AUTOMORPHISM GROUP

Published online by Cambridge University Press:  24 March 2003

SAHARON SHELAH
SAHARON SHELAH
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, [email protected]
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Abstract

It is proved that the automorphism group of a countable structure cannot be a free uncountable group. The idea is that instead of proving that every countable set of equations of a certain form has a solution, it is proved that this holds for a co-meagre family of appropriate countable sets of equations.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 1 , January 2003 , pp. 1 - 7
Copyright
© The London Mathematical Society 2003

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Footnotes

This research was partially supported by the Israel Science Foundation.