In model theory, a branch of mathematical logic, a theory is κ-categorical (or categorical in &kappa) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley which states that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities.

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  • In model theory, a branch of mathematical logic, a theory is κ-categorical (or categorical in &kappa) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley which states that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities. Saharon Shelah extended Morley's theorem to uncountable languages: if the language has cardinality κ and a theory is categorical in some uncountable cardinal greater than or equal to κ then it is categorical in all cardinalities greater than κ.
  • Morleyova věta o kategoričnosti je jednou z nejdůležitějších vět teorie modelů. Dokázal ji roku 1962 americký matematik Michael Darwin Morley ve své disertační práci s názvem „Categoricity in Power“. Tuto větu později zobecnil Saharon Shelah.
  • Inom modellteorin sägs en teori vara kategorisk om den upp till isomorfi har en unik modell. En teori sägs vara kategorisk i en viss kardinalitet om den upp till isomorfi har en unik modell i denna kardinalitet
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  • E.A.
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  • c/c020730
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  • Palyutin
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  • Categoricity in cardinality
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  • In model theory, a branch of mathematical logic, a theory is κ-categorical (or categorical in &kappa) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley which states that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities.
  • Morleyova věta o kategoričnosti je jednou z nejdůležitějších vět teorie modelů. Dokázal ji roku 1962 americký matematik Michael Darwin Morley ve své disertační práci s názvem „Categoricity in Power“. Tuto větu později zobecnil Saharon Shelah.
  • Inom modellteorin sägs en teori vara kategorisk om den upp till isomorfi har en unik modell. En teori sägs vara kategorisk i en viss kardinalitet om den upp till isomorfi har en unik modell i denna kardinalitet
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  • Morley's categoricity theorem
  • Morleyova věta o kategoričnosti
  • Kategorisk teori
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