Uncountable Dense Categoricity in Cats

Journal of Symbolic Logic 70 (3):829 - 860 (2005)
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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DOI 10.2178/jsl/1122038916
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Byunghan Kim & Anand Pillay (1997). Simple Theories. Annals of Pure and Applied Logic 88 (2):149-164.
Itay Ben-Yaacov (2003). Simplicity in Compact Abstract Theories. Journal of Mathematical Logic 3 (02):163-191.

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