Realization of φ -types and Keisler’s order

Annals of Pure and Applied Logic 157 (2-3):220-224 (2009)

Abstract
We show that the analysis of Keisler’s order can be localized to the study of φ-types. Specifically, if is a regular ultrafilter on λ such that and M is a model whose theory is countable, then is λ+-saturated iff it realizes all φ-types of size λ
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DOI 10.1016/j.apal.2008.09.008
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References found in this work BETA

Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
Ultraproducts Which Are Not Saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.
Saturation of Ultrapowers and Keisler's Order.Saharon Shelah - 1972 - Annals of Pure and Applied Logic 4 (1):75.

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Citations of this work BETA

The Characteristic Sequence of a First-Order Formula.M. E. Malliaris - 2010 - Journal of Symbolic Logic 75 (4):1415-1440.
Hypergraph Sequences as a Tool for Saturation of Ultrapowers.M. E. Malliaris - 2012 - Journal of Symbolic Logic 77 (1):195-223.
Edge Distribution and Density in the Characteristic Sequence.M. E. Malliaris - 2010 - Annals of Pure and Applied Logic 162 (1):1-19.

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