Uncountable Dense Categoricity in Cats

Journal of Symbolic Logic 70 (3):829 - 860 (2005)
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Abstract

We prove that under reasonable assumptions, every cat (compact abstract theory) is metric, and develop some of the theory of metric cats. We generalise Morley's theorem: if a countable Hausdorff cat T has a unique complete model of density character Λ ≥ ω₁, then it has a unique complete model of density character Λ for every Λ ≥ ω₁

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10.2178/jsl/1122038916

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Citations of this work

Positive Jonsson Theories.Bruno Poizat & Aibat Yeshkeyev - 2018 - Logica Universalis 12 (1-2):101-127.
Categoricity in homogeneous complete metric spaces.Åsa Hirvonen & Tapani Hyttinen - 2009 - Archive for Mathematical Logic 48 (3-4):269-322.
On Stable Quotients.Krzysztof Krupiński & Adrián Portillo - 2022 - Notre Dame Journal of Formal Logic 63 (3):373-394.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Positive model theory and compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (01):85-118.
Simplicity in compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.

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