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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Weakly homogeneous models

Author: Anand Pillay
Journal: Proc. Amer. Math. Soc. 86 (1982), 126-132
MSC: Primary 03C45; Secondary 03C15, 03C50
MathSciNet review: 663881
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Abstract: I consider some notions of weak homogeneity, which generalise $ \omega $-homogeneity. I first analyse a specific such notion, called almost homogeneity, in the context of $ \omega $-stable theories. (Almost homogeneity is just like $ \omega $-homogeneity, but using strong types in place of types.) Then in a more general context, I prove for weakly homogeneous countable models some classification results which are known for $ \omega $-homogeneous countable models, in particular the result that the isomorphism type of such a model is determined by the types which it realises.

References [Enhancements On Off] (What's this?)

  • [1] E. Bouscaren and D. Lascar, The countable models of a non-multidimensional $ \omega $-stable theory (to appear).
  • [2] D. Lascar and B. Poizat, An introduction to forking, J. Symbolic Logic 44 (1979), 330-350. MR 540665 (80k:03030)
  • [3] S. Shelah, Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978. MR 513226 (81a:03030)

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Keywords: Strong type, $ \omega $-stable, almost homogeneous, $ E$-homogeneous
Article copyright: © Copyright 1982 American Mathematical Society

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