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External automorphisms of ultraproducts of finite models

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Abstract

Let \({\fancyscript{L}}\) be a finite first-order language and \({\langle{\fancyscript{M}_n} \,|\, {n < \omega}\rangle}\) be a sequence of finite \({\fancyscript{L}}\)-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 \({\fancyscript{U}}\) over ω such that the corresponding ultraproduct \({\prod_\fancyscript{U}\fancyscript{M}_n}\) has an automorphism that is not induced by an element of \({\prod_{n<\omega}{\rm Aut}(\fancyscript{M}_n)}\) .

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Correspondence to Philipp Lücke.

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Lücke, P., Shelah, S. External automorphisms of ultraproducts of finite models. Arch. Math. Logic 51, 433–441 (2012). https://doi.org/10.1007/s00153-012-0271-1

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  • DOI: https://doi.org/10.1007/s00153-012-0271-1

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