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: [set theory, hasAxiomSystem, Zermelo–Fraenkel set theory]

Target entity: Zermelo–Fraenkel set theory
Context triple: [set theory, hasAxiomSystem, 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. 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. 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. Foundations of Set Theory (with Andrey Kolmogorov)
  "Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasAxiomSystem
Context triple: [set theory, hasAxiomSystem, Zermelo–Fraenkel set theory]

• A. hasAxiom
  Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
• B. foundationAxiomHoldsIn
  Indicates that the foundation (or regularity) axiom is satisfied within a given model, structure, or context.
• C. logicSystem chosen
  Indicates a relationship where an entity is associated with, defined within, or governed by a particular logical framework or system of formal reasoning.
• D. hasTypeSystem
  Indicates that an entity employs, is governed by, or is associated with a particular type system (a defined set of rules for classifying and constraining types).
• E. hasTheorem
  Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
• F. None of above.