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The number of non-isomorphic models of an unstable first-order theory

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Abstract

It is proved that ifT is an unstable (first-order) theory,λ>|T|+ℵ0, thenT has exactly 2λ non-isomorphic models of cardinalityλ. In fact we have stronger results: this is true for pseudo-elementary classes, and for almost everyλ≧|T|+ℵ1.

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The preparation of this paper was sponsored in part by NSF Grant GP-22937. This work was supported in part by NSF Grant GP-22794.

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Shelah, S. The number of non-isomorphic models of an unstable first-order theory. Israel J. Math. 9, 473–487 (1971). https://doi.org/10.1007/BF02771463

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  • DOI: https://doi.org/10.1007/BF02771463

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