### External Automorphisms of Ultraproducts of Finite Models

by Luecke and Shelah. [LcSh:982]

Archive for Math Logic, 2012

Let {L} be a finite first-order language and
<{{M}_n}{n< omega}> be a sequence of finite
{L}-models containing models of arbitrarily large finite
cardinality. If the intersection of less than continuum-many
dense open subsets of Cantor Space {}^omega 2 is non-empty,
then there is a non-principal ultrafilter {U} over
omega such that the corresponding ultraproduct
prod_{{U}} {M}_n is infinite and has an
automorphism that is not induced by an element of prod_{n< omega}
Aut {{M}_n} .

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