External automorphisms of ultraproducts of finite models

Philipp Lücke*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let L be a finite first-order language and 〈M n {pipe} n < ω〉 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 ω2 is non-empty, 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 Π n<ω Aut(M n).

Original languageEnglish
Pages (from-to)433-441
Number of pages9
JournalArchive for Mathematical Logic
Volume51
Issue number3-4
DOIs
StatePublished - May 2012

Keywords

  • Automorphisms
  • Ultraproducts

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