Keisler’s order via Boolean ultrapowers

Archive for Mathematical Logic 60 (3):425-439 (2020)
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Abstract

In this paper, we provide a new characterization of Keisler’s order in terms of saturation of Boolean ultrapowers. To do so, we apply and expand the framework of ‘separation of variables’ recently developed by Malliaris and Shelah. We also show that good ultrafilters on Boolean algebras are precisely the ones which capture the maximum class in Keisler’s order, answering a question posed by Benda in 1974.

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2021

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10.1007/s00153-020-00750-7

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References found in this work

Ultraproducts which are not saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.
The theory of Boolean ultrapowers.Richard Mansfield - 1971 - Annals of Mathematical Logic 2 (3):297-323.
Reduced Direct Products.T. Frayne, A. C. Morel & D. S. Scott - 1966 - Journal of Symbolic Logic 31 (3):506-507.
The theory of boolean ultrapowers.Richard Mansfield - 1971 - Annals of Mathematical Logic 2 (3):297.
Ultraproducts and Saturated Models.H. Jerome Keisler - 1970 - Journal of Symbolic Logic 35 (4):584-585.

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