Categoricity for abstract classes with amalgamation

Saharon Shelah

doi:10.1016/S0168-0072(98)00016-5

Categoricity for abstract classes with amalgamation

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

69 Scopus citations

Abstract

Let elf be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS(elf). We prove that for a suitable Hanf number χ₀ if χ₀ < λ₀ ≤ λ₁ and elf is categorical in λ⁺₁ then it is categorical in λ₀.

Original language	English
Pages (from-to)	261-294
Number of pages	34
Journal	Annals of Pure and Applied Logic
Volume	98
Issue number	1-3
DOIs	https://doi.org/10.1016/S0168-0072(98)00016-5
State	Published - 30 Jun 1999

Keywords

Abstract elementary classes
Categoricity
Classifying non-first order classes
Hanf numbers

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10.1016/S0168-0072(98)00016-5

Cite this

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title = "Categoricity for abstract classes with amalgamation",

abstract = "Let elf be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS(elf). We prove that for a suitable Hanf number χ0 if χ0 < λ0 ≤ λ1 and elf is categorical in λ+1 then it is categorical in λ0.",

keywords = "Abstract elementary classes, Categoricity, Classifying non-first order classes, Hanf numbers",

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AB - Let elf be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS(elf). We prove that for a suitable Hanf number χ0 if χ0 < λ0 ≤ λ1 and elf is categorical in λ+1 then it is categorical in λ0.

KW - Abstract elementary classes

KW - Categoricity

KW - Classifying non-first order classes

KW - Hanf numbers

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JO - Annals of Pure and Applied Logic

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Categoricity for abstract classes with amalgamation

Abstract

Keywords

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