Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] Daniel Lascar and Bruno Poizat, An introduction to forking, J. Symbolic Logic 44 (1979), no. 3, 330–350. MR 540665, 10.2307/2273127
  • [3] Saharon Shelah, Classification theory and the number of nonisomorphic models, Studies in Logic and the Foundations of Mathematics, vol. 92, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 513226

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03C45, 03C15, 03C50

Retrieve articles in all journals with MSC: 03C45, 03C15, 03C50

Additional Information

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