On the existence of saturated models of stable theories

On the existence of saturated models of stable theories
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Proc. Amer. Math. Soc. 52 (1975), 361-367

DOI: https://doi.org/10.1090/S0002-9939-1975-0387043-7

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

References

J. T. Baldwin and Andreas Blass, An axiomatic approach to rank in model theory, Ann. Math. Logic 7 (1974), 295–324. MR 363875, DOI 10.1016/0003-4843(74)90018-7

Stable theories and related concepts

Victor Harnik and Jean-Pierre Ressayre, Prime extensions and categoricity in power, Israel J. Math. 10 (1971), 172–185. MR 300885, DOI 10.1007/BF02771568
Michael Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514–538. MR 175782, DOI 10.1090/S0002-9947-1965-0175782-0
J. P. Ressayre, Sur les théories du premier ordre catégoriques en un cardinal, Trans. Amer. Math. Soc. 142 (1969), 481–505 (French). MR 246762, DOI 10.1090/S0002-9947-1969-0246762-5
S. Shelah, Stable theories, Israel J. Math. 7 (1969), 187–202. MR 253889, DOI 10.1007/BF02787611
Saharon Shelah, Finite diagrams stable in power, Ann. Math. Logic 2 (1970/71), no. 1, 69–118. MR 285374, DOI 10.1016/0003-4843(70)90007-0
Saharon Shelah, Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory, Ann. Math. Logic 3 (1971), no. 3, 271–362. MR 317926, DOI 10.1016/0003-4843(71)90015-5
Saharon Shelah, Saturation of ultrapowers and Keisler’s order, Ann. Math. Logic 4 (1972), 75–114. MR 294113, DOI 10.1016/0003-4843(72)90012-5