# Sh:982

• Lücke, P., & Shelah, S. (2012). External automorphisms of ultraproducts of finite models. Arch. Math. Logic, 51(3-4), 433–441.
• Abstract:
Let \mathcal{L} be a finite first-order language and \langle{\mathcal{M}_n}{n<\omega}\rangle be a sequence of finite \mathcal{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 \mathcal{U} over \omega such that the corresponding ultraproduct \prod_{\mathcal{U}} \mathcal{M}_n is infinite and has an automorphism that is not induced by an element of \prod_{n<\omega} {\rm Aut}{\mathcal{M}_n}.
• Version 2011-03-18_11 (7p) published version (9p)
Bib entry
@article{Sh:982,
author = {L{\"u}cke, Philipp and Shelah, Saharon},
title = {{External automorphisms of ultraproducts of finite models}},
journal = {Arch. Math. Logic},
fjournal = {Archive for Mathematical Logic},
volume = {51},
number = {3-4},
year = {2012},
pages = {433--441},
issn = {0933-5846},
mrnumber = {2899700},
mrclass = {03C20 (03E50 20B27)},
doi = {10.1007/s00153-012-0271-1}
}