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 incompleteness theorems | Statement: [Peano arithmetic, impliedBy, Gödel incompleteness theorems]

Target entity: Gödel incompleteness theorems
Context triple: [Peano arithmetic, impliedBy, Gödel incompleteness theorems]

• 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. Reflections on Kurt Gödel
  Reflections on Kurt Gödel is a philosophical and biographical study in which logician Hao Wang presents his conversations with and insights about Kurt Gödel’s life, work, and views on logic, mathematics, and philosophy.
• D. 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.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.