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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 λOther Versions
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Citations of this work
The Dividing Line Methodology: Model Theory Motivating Set Theory.John T. Baldwin - 2021 - Theoria 87 (2):361-393.
Hypergraph sequences as a tool for saturation of ultrapowers.M. E. Malliaris - 2012 - Journal of Symbolic Logic 77 (1):195-223.
On positive local combinatorial dividing-lines in model theory.Vincent Guingona & Cameron Donnay Hill - 2019 - Archive for Mathematical Logic 58 (3-4):289-323.
Keisler’s order is not linear, assuming a supercompact.Douglas Ulrich - 2018 - Journal of Symbolic Logic 83 (2):634-641.
Model-theoretic properties of ultrafilters built by independent families of functions.M. Malliaris & S. Shelah - 2014 - Journal of Symbolic Logic 79 (1):103-134.
References found in this work
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 Mathematical Logic 4 (1):75.
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