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: [von Neumann paradox in set theory, usesAxiom, axiom of choice]

Target entity: axiom of choice
Context triple: [von Neumann paradox in set theory, usesAxiom, axiom of choice]

• 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. 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.
• C. Zermelo set theory
  Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
• D. set theory
  Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: axiom of choice
Triple: [von Neumann paradox in set theory, usesAxiom, axiom of choice]

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.

Target entity: axiom of choice
Target entity description: 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.

• 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. 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.
• C. Zermelo set theory
  Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
• D. set theory
  Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
• 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. chosen

Target predicate: usesAxiom
Context triple: [von Neumann paradox in set theory, usesAxiom, axiom of choice]

• A. hasAxiom chosen
  Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
• B. usesPrinciple
  Indicates that one entity applies, relies on, or is based upon a particular principle in its functioning, reasoning, or design.
• C. symbolicallyUses
  Indicates that one entity employs another as a symbol or representation to convey meaning, ideas, or associations rather than for its literal or practical function.
• D. usedByAce
  Indicates that something is utilized or employed by an entity referred to as "Ace."
• E. isUsedAs
  Indicates that one entity serves a particular function, role, or purpose as another entity.
• F. None of above.