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: Bachmann–Howard ordinal | Statement: [Kripke–Platek set theory, hasProofTheoreticOrdinal, Bachmann–Howard ordinal]

Target entity: Bachmann–Howard ordinal
Context triple: [Kripke–Platek set theory, hasProofTheoreticOrdinal, Bachmann–Howard ordinal]

• A. Bachmann–Howard ordinal chosen
  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.
• B. 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.
• C. Cantor normal form
  Cantor normal form is a canonical way of expressing any ordinal number as a finite sum of decreasing powers of the first infinite ordinal ω with natural number coefficients.
• D. Graham's number
  Graham's number is an extraordinarily large number that arose in a problem in Ramsey theory and became famous as one of the largest numbers ever used in a serious mathematical proof.
• E. Ackermann function
  The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasProofTheoreticOrdinal
Context triple: [Kripke–Platek set theory, hasProofTheoreticOrdinal, Bachmann–Howard ordinal]

• A. provedUndecidableUsing
  Indicates that the undecidability of one problem, theory, or statement was established by applying or reducing it to another specific method, result, or formal system.
• B. hasElementaryProof
  Indicates that there exists a proof of the statement using only elementary methods, without relying on advanced or sophisticated theories.
• C. hasTheorem
  Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
• D. wasFirstProvedBy
  Indicates that a particular statement, theorem, or result was originally and for the first time demonstrated or established as true by a specified agent.
• E. hasCanonicalValuation
  Indicates that an entity is associated with its standard or officially recognized valuation or assessed value.
• F. None of above. chosen