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 with choice | Statement: [von Neumann–Bernays–Gödel set theory, isEquiconsistentWith, Zermelo–Fraenkel set theory with choice]

Target entity: Zermelo–Fraenkel set theory with choice
Context triple: [von Neumann–Bernays–Gödel set theory, isEquiconsistentWith, Zermelo–Fraenkel set theory with choice]

• 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. 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.
• C. 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.
• D. Morse–Kelley set theory by class–set distinction
  Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
• E. set theory
  Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: isEquiconsistentWith
Context triple: [von Neumann–Bernays–Gödel set theory, isEquiconsistentWith, Zermelo–Fraenkel set theory with choice]

• A. equivalentTo
  Indicates that two entities represent the same concept, value, or state, and can be treated as interchangeable in the given context.
• B. hasEquivalent
  Indicates that two entities are considered equal in value, meaning, or function within a given context.
• C. isInverseOf
  Indicates that one relation reverses the direction of another, so that if the original relates A to B, its inverse relates B to A.
• D. isInconsistent
  Indicates that there is a logical or factual contradiction within or between the entities or statements involved.
• E. coincidesWith
  Indicates that two entities occupy the same position, time, or state such that they exactly overlap or occur together.
• F. None of above. chosen