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)



Countable models of stable theories

Author: Anand Pillay
Journal: Proc. Amer. Math. Soc. 89 (1983), 666-672
MSC: Primary 03C45; Secondary 03C15
MathSciNet review: 718994
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The notion of a normal theory such a theory $ T,\;I({\aleph _0},T) = 1{\text{ or }} \geqslant {\aleph _0}$. theorem that for superstable $ T,\;I({\aleph _0},T) = 1{\text{ or }} \geqslant {\aleph _0}$ stronger than stability but incomparable is introduced, and it is proved that for We also include a short proof of Lachlan's (The property of normality is to superstability.)

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

  • [1] A. H. Lachlan, The number of countable models of a countable superstable theory, Proc. Internat. Congr. on Logic, Methodology and the Philosophy of Science, North-Holland, Amsterdam, 1973. pp. 45-56. MR 0446949 (56:5266)
  • [2] -, Two conjectures on the stability of $ \omega $-categorial theories, Fund. Math. 81 (1974), 133-145.
  • [3] D. Lascar, Ranks and definability in superstable theories, Israel J. Math. 23 (1976), 53-87. MR 0409169 (53:12931)
  • [4] D. Lascar and B. Poizat, An introduction to forking, J. Symbolic Logic 44 (1979), 330-350. MR 540665 (80k:03030)
  • [5] T. G. Mustafin, Number of countable models of a countable complete theory, Algebra i Logika 20 (1981), 69-91. MR 635651 (84m:03047)
  • [6] A. Pillay, Countable modules, Fund. Math. (to appear). MR 765328 (86c:03029)
  • [7] S. Shelah, Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978. MR 513226 (81a:03030)

Similar Articles

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

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

Additional Information

Keywords: Normal theory, superstable
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society