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: Kripke–Platek set theory with urelements | Statement: [Kripke–Platek set theory, hasConservativeExtension, Kripke–Platek set theory with urelements]

Target entity: Kripke–Platek set theory with urelements
Context triple: [Kripke–Platek set theory, hasConservativeExtension, Kripke–Platek set theory with urelements]

• A. Kripke–Platek set theory chosen
  Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
• B. Fraenkel–Mostowski permutation models
  Fraenkel–Mostowski permutation models are set-theoretic constructions using permutations of atoms to demonstrate the independence of certain choice principles from Zermelo–Fraenkel set theory.
• C. 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.
• D. Set Theory and Its Logic
  Set Theory and Its Logic is a foundational work by W.V.O. Quine that develops set theory within a rigorous logical framework, exploring its axioms, paradoxes, and philosophical implications.
• 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: hasConservativeExtension
Context triple: [Kripke–Platek set theory, hasConservativeExtension, Kripke–Platek set theory with urelements]

• A. isConservativeOver chosen
  Indicates that one entity preserves or does not increase a certain property, measure, or effect when applied over or in relation to another entity.
• B. hasExtensionBy
  Indicates that one entity is extended, augmented, or further developed by another entity.
• C. definesExtension
  Indicates that one entity specifies or establishes the extension, scope, or detailed form of another entity.
• D. includesExtension
  Indicates that one entity contains or incorporates another entity as an added or supplementary extension.
• E. usesExtensionOf
  Indicates that one entity makes use of another entity that is an extension or extended version of something else.
• F. None of above.