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

Saharon Shelah

doi:10.1007/BF02771463

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

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

37 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	473-487
Number of pages	15
Journal	Israel Journal of Mathematics
Volume	9
Issue number	4
DOIs	https://doi.org/10.1007/BF02771463
State	Published - Feb 1971

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

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

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

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