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On the number of homogeneous models of a given power

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Abstract

It is shown that, For each complete theoryT, the nomberh T(m) of homogeneous models ofT of powerm is a non-increasing function of uncountabel cardinalsm Moreover, ifh T(ℵ0)≦ℵ0, then the functionh T is also non-increasing ℵ0 to ℵ1.

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Authors and Affiliations

  1. University of Wisconsin, Madison, Wisconsin

    H. Jerome Keisler & Michael D. Morley

Authors
  1. H. Jerome Keisler
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  2. Michael D. Morley
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Additional information

This work was supported in part by NSF contracts GP 4257 and GP5913.

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Keisler, H.J., Morley, M.D. On the number of homogeneous models of a given power. Israel J. Math. 5, 73–78 (1967). https://doi.org/10.1007/BF02771624

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  • DOI: https://doi.org/10.1007/BF02771624

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