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: incompleteness theorems | Statement: [Kurt Gödel, knownFor, incompleteness theorems]

Target entity: incompleteness theorems
Context triple: [Kurt Gödel, knownFor, 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. 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.
• D. completeness theorem for first-order logic
  The completeness theorem for first-order logic is a fundamental result in mathematical logic, proved by Kurt Gödel, which states that every logically valid first-order formula is provable from the axioms of first-order logic.
• E. Gödel numbering
  Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.