Existence of many L∞,λ-equivalent, non- isomorphic models of T of power λ

Saharon Shelah

doi:10.1016/0168-0072(87)90005-4

Existence of many L_∞,λ-equivalent, non- isomorphic models of T of power λ

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

Suppose T is not superstable, T ⊆ T₁ (both first-order theories). If λ>∥T₁∥ is regular or strong limit, we construct 2^λ non-isomorphic, pairwise L_∞,λ-equivalent models of T of power λ, which are reducts of models of T₁. Note, however, that the proof applies to the class of models of T, T (superstable but) with dop or otop and even to appropriate non-elementary classes as well.

Original language	English
Pages (from-to)	291-310
Number of pages	20
Journal	Annals of Pure and Applied Logic
Volume	34
Issue number	3
DOIs	https://doi.org/10.1016/0168-0072(87)90005-4
State	Published - Jun 1987

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abstract = "Suppose T is not superstable, T ⊆ T1 (both first-order theories). If λ>∥T1∥ is regular or strong limit, we construct 2λ non-isomorphic, pairwise L∞,λ-equivalent models of T of power λ, which are reducts of models of T1. Note, however, that the proof applies to the class of models of T, T (superstable but) with dop or otop and even to appropriate non-elementary classes as well.",

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N2 - Suppose T is not superstable, T ⊆ T1 (both first-order theories). If λ>∥T1∥ is regular or strong limit, we construct 2λ non-isomorphic, pairwise L∞,λ-equivalent models of T of power λ, which are reducts of models of T1. Note, however, that the proof applies to the class of models of T, T (superstable but) with dop or otop and even to appropriate non-elementary classes as well.

AB - Suppose T is not superstable, T ⊆ T1 (both first-order theories). If λ>∥T1∥ is regular or strong limit, we construct 2λ non-isomorphic, pairwise L∞,λ-equivalent models of T of power λ, which are reducts of models of T1. Note, however, that the proof applies to the class of models of T, T (superstable but) with dop or otop and even to appropriate non-elementary classes as well.

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Existence of many L_∞,λ-equivalent, non- isomorphic models of T of power λ

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