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: Zermelo–Fraenkel set theory by treating the collection of all ordinals as a proper class | Statement: [Burali-Forti paradox, resolvedIn, Zermelo–Fraenkel set theory by treating the collection of all ordinals as a proper class]

Target entity: Zermelo–Fraenkel set theory by treating the collection of all ordinals as a proper class
Context triple: [Burali-Forti paradox, resolvedIn, Zermelo–Fraenkel set theory by treating the collection of all ordinals as a proper class]

• A. Zermelo–Fraenkel set theory
  Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
• B. von Neumann–Bernays–Gödel set theory chosen
  Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
• C. von Neumann universe
  The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
• D. von Neumann paradox in set theory
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• E. Burali-Forti paradox
  The Burali-Forti paradox is a foundational logical contradiction in set theory that arises from considering the set of all ordinal numbers, showing that such a totality cannot consistently exist as a set.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: resolvedIn
Context triple: [Burali-Forti paradox, resolvedIn, Zermelo–Fraenkel set theory by treating the collection of all ordinals as a proper class]

• A. resolves
  Indicates that one entity successfully finds a solution, answer, or outcome for a problem, conflict, or uncertainty involving another entity.
• B. resolution
  Indicates the act of formally deciding, settling, or expressing a determined stance on an issue, often through an official decision or statement.
• C. settled
  Indicates that an entity established residence or a stable presence in a place, typically after moving from elsewhere.
• D. notableResolution
  Indicates that an entity is distinguished or recognized for having a particularly important, impactful, or well-known resolution or decision.
• E. concluded
  Indicates that an entity has brought an event, process, discussion, or agreement to an end, often after reaching a decision or final judgment.
• F. None of above. chosen