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: [The Consistency of the Continuum Hypothesis, mainTopic, Axiom of Choice]

Target entity: Axiom of Choice
Context triple: [The Consistency of the Continuum Hypothesis, mainTopic, 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. 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.
• C. Axiom of Extensionality in set theory
  The Axiom of Extensionality in set theory states that a set is completely determined by its members, meaning two sets are equal if and only if they have exactly the same elements.
• D. 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.
• E. Ultrafilter lemma
  The ultrafilter lemma is a set-theoretic principle weaker than the full Axiom of Choice that guarantees every filter can be extended to an ultrafilter and underlies several key results in topology and analysis.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.