Abstract
We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated models of uncountable first-order theories). We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.
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This research was made possible partially by Colciencias grant Métodos de Estabilidad en Clases No Estables. The first author’s research was also partially supported by the Iran National Science Foundation (INSF).
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Ghadernezhad, Z., Villaveces, A. The small index property for homogeneous models in AEC’s. Arch. Math. Logic 57, 141–157 (2018). https://doi.org/10.1007/s00153-017-0587-y
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DOI: https://doi.org/10.1007/s00153-017-0587-y