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} .

Back to the list of publications