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- W4241891780 abstract "Abstract We get consistency results on I ( λ, T, T ) under the assumption that D ( T ) has cardinality > ∣ T ∣. We get positive results and consistency results on IE ( λ, T 1 , T ). The interest is model-theoretic, but the content is mostly set-theoretic: in Theorems 1–3, combinatorial; in Theorems 4–7 and 11(2), to prove consistency of counterexamples we concentrate on forcing arguments; and in Theorems 8–10 and 11(1), combinatorics for counterexamples; the rest are discussion and problems. In particular: (A) By Theorems 1 and 2, if T ⊆ T 1 are first order countable, T complete stable but ℵ 0 -unstable, λ > ℵ 0 , and ∣ D ( T )∣ > ℵ 0 , then IE ( λ, T 1 , T ) > Min{2 λ , ℶ 2 }. (B) By Theorems 4,5,6 of this paper, if e.g. V = L , then in some generic extension of V not collapsing cardinals, for some first order T ⊆ T 1 , ∣ T ∣ = ℵ 0 , ∣ T 1 ∣ = ℵ 1 , ∣ D ( T )∣ = ℵ 2 and IE (ℵ 2 , T 1 , T ) = 1. This paper (specifically the ZFC results) is continued in the very interesting work of Baldwin on diversity classes [Bl]. Some more advances can be found in the new version of [Sh300] (see Chapter III, mainly §7); they confirm 0.1, 0.2 and 14(1), 14(2)." @default.
- W4241891780 created "2022-05-12" @default.
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- W4241891780 date "1989-12-01" @default.
- W4241891780 modified "2023-09-27" @default.
- W4241891780 title "The number of pairwise non-elementarily-embeddable models" @default.
- W4241891780 doi "https://doi.org/10.2307/2274824" @default.
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