Morley’s Categoricity Theorem
نویسنده
چکیده
A theory is called κ-categorical, or categorical in power κ, if it has one model up to isomorphism of cardinality κ. Morley’s Categoricity Theorem states that if a theory of first order logic is categorical in some uncountable power κ, then it is categorical in every uncountable power. We provide an elementary exposition of this theorem, by showing that a theory is categorical in some uncountable power if and only if it is ω-stable and has no Vaughtian pairs. Along the way, we will develop the theory of Vaughtian pairs, stable theories, and indiscernibles and provide a proof of Vaught’s two-cardinal theorem.
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