Sh:982

• Lücke, P., & Shelah, S. (2012). External automorphisms of ultraproducts of finite models. Arch. Math. Logic, 51(3-4), 433–441. DOI: 10.1007/s00153-012-0271-1 MR: 2899700
• 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)

@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}
}