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: Gödel’s second incompleteness theorem | Statement: [Hilbert’s second problem, connectedToResult, Gödel’s second incompleteness theorem]

Target entity: Gödel’s second incompleteness theorem
Context triple: [Hilbert’s second problem, connectedToResult, Gödel’s second incompleteness theorem]

• A. Gödel's incompleteness theorems chosen
  Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
• B. Tarski's undefinability theorem
  Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
• C. Gentzen’s consistency proof for arithmetic
  Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
• D. Löb's theorem
  Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
• E. Hilbert’s program
  Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: connectedToResult
Context triple: [Hilbert’s second problem, connectedToResult, Gödel’s second incompleteness theorem]

• A. connectionTo
  Indicates a relationship in which one entity is linked, associated, or otherwise related to another entity.
• B. connectedToEvent
  Indicates that an entity has a direct association or linkage with a specific event.
• C. connectsState
  Indicates a relationship where one entity serves as a link or conduit between different states, conditions, or statuses of another entity.
• D. notConnectedBy
  Indicates that there is no direct link, path, or relationship connecting the referenced entities.
• E. connectsTo chosen
  Indicates a relationship where one entity is linked or joined to another, allowing interaction, communication, or transfer between them.
• F. None of above.