Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Morley rank | Statement: [model theory, hasKeyConcept, Morley rank]

Target entity: Morley rank
Context triple: [model theory, hasKeyConcept, Morley rank]

• A. Vaught conjecture
  The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
• B. Vaught transforms in model theory
  Vaught transforms in model theory are a technical construction introduced by Robert Vaught that modify formulas to analyze their behavior across models, particularly in the study of completeness, definability, and related model-theoretic properties.
• C. Suslin rigidity theorem
  The Suslin rigidity theorem is a fundamental result in algebraic K-theory asserting strong invariance (rigidity) properties of K-theory for certain rings or schemes under extensions or deformations.
• D. Tarski–Mostowski–Robinson theorem
  The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
• E. Łoś–Tarski preservation theorem
  The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Morley rank
Target entity description: Morley rank is a model-theoretic notion of dimension that assigns an ordinal-valued measure of complexity to definable sets in a structure.

• A. Vaught conjecture
  The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
• B. Vaught transforms in model theory
  Vaught transforms in model theory are a technical construction introduced by Robert Vaught that modify formulas to analyze their behavior across models, particularly in the study of completeness, definability, and related model-theoretic properties.
• C. Suslin rigidity theorem
  The Suslin rigidity theorem is a fundamental result in algebraic K-theory asserting strong invariance (rigidity) properties of K-theory for certain rings or schemes under extensions or deformations.
• D. Tarski–Mostowski–Robinson theorem
  The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
• E. Łoś–Tarski preservation theorem
  The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
• F. None of above. chosen