The Keisler order in continuous logic

DOI10.1007/s41980-022-00690-3OpenAlexW4220665471MaRDI QIDQ2682715

Mary Leah Karker, Nathanael Leedom Ackerman

Publication date: 1 February 2023

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41980-022-00690-3

zbMATH Keywords

ultraproductscontinuous logicreduced productsKeisler ordercomplete metric structures

Mathematics Subject Classification ID

Complete metric spaces (54E50) Ultraproducts and related constructions (03C20) Continuous model theory, model theory of metric structures (03C66)

Cites Work

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• Existence of optimal ultrafilters and the fundamental complexity of simple theories
• Realization of \(\varphi \)-types and Keisler's order
• Classification theory and the number of non-isomorphic models.
• Keisler's order has infinitely many classes
• \(l\)-groups \(C(X)\) in continuous logic
• Encoding complete metric structures by classical structures
• Keisler's order is not simple (and simple theories may not be either)
• Metric Scott analysis
• A dividing line within simple unstable theories
• REDUCED PRODUCTS OF METRIC STRUCTURES: A METRIC FEFERMAN–VAUGHT THEOREM
• Reduced products and sheaves of metric structures
• A Maximality Theorem for Continuous First Order Theories
• A presentation theorem for continuous logic and metric abstract elementary classes
• Ultraproducts which are not saturated
• Using ultrapowers to compare continuous structures

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