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: axiom of choice | Statement: [Cauchy functional equation, pathologicalSolutionsDependOn, axiom of choice]

Target entity: axiom of choice
Context triple: [Cauchy functional equation, pathologicalSolutionsDependOn, axiom of choice]

• A. axiom of choice chosen
  The axiom of choice is a fundamental principle in set theory asserting that one can select an element from each set in any collection of nonempty sets, with far-reaching consequences across mathematics.
• B. 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.
• C. axiom schema of separation
  The axiom schema of separation is a principle in set theory that guarantees the existence of subsets defined by properties or predicates, helping to avoid paradoxes by restricting unrestricted set formation.
• D. Hausdorff maximal principle
  The Hausdorff maximal principle is a foundational result in set theory and order theory stating that every partially ordered set contains a maximal totally ordered subset (a maximal chain), and it is equivalent to the axiom of choice.
• E. continuum hypothesis
  The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: pathologicalSolutionsDependOn
Context triple: [Cauchy functional equation, pathologicalSolutionsDependOn, axiom of choice]

• A. basedOnSolutionOf
  Indicates that one entity is derived, developed, or constructed using the solution or outcome produced by another entity.
• B. providesSolutionFor
  Indicates that one entity offers or supplies a remedy, answer, or resolution to a problem, need, or issue associated with another entity.
• C. commonlySolvedBy
  Indicates that a problem, task, or issue is typically addressed or resolved through a particular method, tool, or agent.
• D. positionDependsOn
  Indicates that the spatial or ordered position of one entity is determined or constrained by the position of another entity.
• E. solutionType
  Indicates the specific category or kind of solution associated with an entity or problem.
• F. None of above. chosen