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High and Low Homogeneity

Abstract

We find conditions such that every \(\lambda \)-homogeneous model with small \( \lambda \) satisfying these conditions is homogeneous. As a corollary, we obtain conditions guaranteeing that the following implication holds: If \(T \) is a theory, \(\mu >|T| \), and every model of \(T \) of cardinality \( \mu \) is \(\omega _1\) -homogeneous then every model of \(T\) of sufficiently large cardinality is homogeneous.

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Correspondence to K. Zh. Kudaĭbergenov.

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Kudaĭbergenov, K.Z. High and Low Homogeneity. Sib. Adv. Math. 31, 13–26 (2021). https://doi.org/10.1134/S1055134421010028

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Keywords

  • homogeneous model
  • lambda-homogeneous model
  • stable theory