# 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)

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} }