The number of non-isomorphic models of an unstable first-order theory |
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| Authors: | Saharon Shelah |
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| Institution: | (1) The Hebrew University of Jerusalem, Israel;(2) Princeton University, Princeton, N.J.;(3) University of California, Los Angeles |
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| Abstract: | It is proved that ifT is an unstable (first-order) theory,λ>|T|+ℵ0, thenT has exactly 2
λ
non-isomorphic models of cardinalityλ. In fact we have stronger results: this is true for pseudo-elementary classes, and for almost everyλ≧|T|+ℵ1.
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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