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)

 
 

 

On the existence of saturated models of stable theories


Author: Victor Harnik
Journal: Proc. Amer. Math. Soc. 52 (1975), 361-367
MSC: Primary 02H05; Secondary 02H20
DOI: https://doi.org/10.1090/S0002-9939-1975-0387043-7
MathSciNet review: 0387043
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proven that a theory $ T$ stable in a power $ \lambda $, $ \lambda > \vert T\vert$, has a saturated model of cardinality $ \lambda $.


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

  • 1. J. T. Baldwin and A. Blass, An axiomatic approach to rank in model theory Ann. Math. Logic 7 (1974), 295-324. MR 0363875 (51:130)
  • [1] V. Harnik, Stable theories and related concepts, Ph.D. Thesis, Hebrew University, 1971.
  • [2] V. Harnik and J.-P. Ressayre, Prime extensions and categoricity in power, Israel J. Math. 10 (1971), 172-185. MR 46 #45. MR 0300885 (46:45)
  • [3] M. D. Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514-538. MR 31 #58. MR 0175782 (31:58)
  • [4] J. P. Ressayre, Sur les théories du premier ordre catégoriques en un cardinal, Trans. Amer. Math. Soc. 142 (1969), 481-505. MR 40 #32. MR 0246762 (40:32)
  • [5] S. Shelah, Stable theories, Israel J. Math. 7 (1969), 187-202. MR 40 #7102. MR 0253889 (40:7102)
  • [6] S. Shelah, Finite diagrams stable in power, Ann. Math. Logic 2 (1970/71), no. 1, 69-118. MR 44 #2593. MR 0285374 (44:2593)
  • [7] -, Stability, the f.c.p. and superstability; model theoretic propreties of formulas in first order theory, Ann. Math. Logic 3 (1971), no. 3, 271-362. MR 47 #6475. MR 0317926 (47:6475)
  • [8] -, Saturation of ultrapowers and Keisler's order, Ann. Math. Logic 4 (1972), 75-114. MR 45 #3187. MR 0294113 (45:3187)
  • [9] -, North-Holland, Amsterdam (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02H05, 02H20

Retrieve articles in all journals with MSC: 02H05, 02H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0387043-7
Keywords: Stable theory, saturated model
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society