Open Access
July 1992 Small models
George Weaver
Mod. Log. 2(4): 351-364 (July 1992).


This paper surveys some problems in the model theory of uncountable first order languages. These problems were first raised in Mal'cev. Their solutions involve the construction of infinite models which are "small" relative to the cardinality of their language. The most important of these problems concern extending the Upward Löwenheim- Skolem Theorem for uncountable languages. The earliest results relevant to this problem used the ultraproduct construction to obtain "small" elementary extensions. Stronger results have been obtained more recently by other methods. These are used to construct "small" elementary subsystems.


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George Weaver. "Small models." Mod. Log. 2 (4) 351 - 364, July 1992.


Published: July 1992
First available in Project Euclid: 6 March 2008

zbMATH: 0765.03018
MathSciNet: MR1172917

Primary: 03-03
Secondary: 01A65 , 03C07 , 03C55

Rights: Copyright © 1992 The Review of Modern Logic

Vol.2 • No. 4 • July 1992
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