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: Woodin cardinal | Statement: [Hugh Woodin, notableConcept, Woodin cardinal]

Target entity: Woodin cardinal
Context triple: [Hugh Woodin, notableConcept, Woodin cardinal]

• A. Feferman–Schütte ordinal
  The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
• B. Bachmann–Howard ordinal
  The Bachmann–Howard ordinal is a large countable ordinal that serves as a key benchmark in proof theory, marking the strength of powerful formal systems extending predicative arithmetic.
• C. Vaught conjecture
  The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
• D. Kripke–Platek set theory
  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.
• E. continuum hypothesis
  The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Woodin cardinal
Target entity description: A Woodin cardinal is a large cardinal in set theory with strong consistency and determinacy properties, central to modern research on the foundations of mathematics and descriptive set theory.

• A. Feferman–Schütte ordinal
  The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
• B. Bachmann–Howard ordinal
  The Bachmann–Howard ordinal is a large countable ordinal that serves as a key benchmark in proof theory, marking the strength of powerful formal systems extending predicative arithmetic.
• C. Vaught conjecture
  The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
• D. Kripke–Platek set theory
  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.
• E. continuum hypothesis
  The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
• F. None of above. chosen