External automorphisms of ultraproducts of finite models

Lücke Philipp, Shelah Saharon

Abstract

Let L be a finite first-order language and 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 is nonempty, then there is a non-principal ultrafilter U over ω such that the corresponding ultraproduct Π_U M_n has an automorphism that is not induced by an element of .