On theories categorical in their own power

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1971 English Publisher:Cambridge University Press (CUP)Journal:Journal of Symbolic Logic, volume 36, pages 240-244 (issn: 0022-4812, eissn: 1943-5886,

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Authors: H. Jerome Keisler;

doi: 10.2307/2270258

On theories categorical in their own power

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Abstract

A theory T is said to be categorical in power κ iff T has a model of power κ and any two models of power κ are isomorphic.It was conjectured by Morley [4] that if T is a theory in a language with κ > ω symbols and T is categorical in power κ, then T has a model of power < κ. The aim of this paper is to prove the following theorem.Theorem A. Let κ be a regular cardinal such that ω < κ < 2ω. Let T be a theory in a language with κ symbols such that T is categorical in power κ. Then:(a) T has a model of power < κ.(b) T is categorical in all powers μ ≥ κ.

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University of Wisconsin–Madison
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University of Wisconsin–Oshkosh
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Keywords

Categoricity and completeness of theories

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