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 | Statement: [Cantor’s paradox, avoidedIn, Zermelo–Fraenkel set theory]

Target entity: Zermelo–Fraenkel set theory
Context triple: [Cantor’s paradox, avoidedIn, Zermelo–Fraenkel set theory]

• A. Zermelo–Fraenkel set theory chosen
  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
  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. Cantor’s theorem
  Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: avoidedIn
Context triple: [Cantor’s paradox, avoidedIn, Zermelo–Fraenkel set theory]

• A. excludes
  Indicates that one entity deliberately omits, leaves out, or does not allow the inclusion of another entity within a set, group, or context.
• B. avoidsRoute
  Indicates that an entity deliberately does not use or travel along a particular route.
• C. prevented
  Indicates that one entity stopped, hindered, or made it impossible for another entity or event to occur or proceed.
• D. prohibits
  Indicates that one entity forbids or disallows another entity from performing a specific action or being in a certain state.
• E. notObservedIn chosen
  Indicates that a particular entity, event, or property has not been detected, recorded, or seen within a specified context, dataset, or environment.
• F. None of above.