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: von Neumann–Bernays–Gödel set theory by class–set distinction | Statement: [Burali-Forti paradox, resolvedIn, von Neumann–Bernays–Gödel set theory by class–set distinction]

Target entity: von Neumann–Bernays–Gödel set theory by class–set distinction
Context triple: [Burali-Forti paradox, resolvedIn, von Neumann–Bernays–Gödel set theory by class–set distinction]

• A. von Neumann–Bernays–Gödel set theory chosen
  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.
• B. von Neumann paradox in set theory
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• C. 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.
• D. 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.
• E. von Neumann universe
  The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.