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: Löb's theorem | Statement: [arithmetization of syntax, relatedConcept, Löb's theorem]

Target entity: Löb's theorem
Context triple: [arithmetization of syntax, relatedConcept, Löb's theorem]

• A. Löb's theorem chosen
  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.
• B. Gödel–Löb provability logic (GL)
  Gödel–Löb provability logic (GL) is a modal logic system that formalizes reasoning about provability in arithmetic, capturing the behavior of the provability predicate in Peano Arithmetic.
• C. 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.
• D. Gödel's incompleteness theorems
  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.
• E. Hilbert–Bernays derivability conditions
  The Hilbert–Bernays derivability conditions are a set of formal requirements on provability predicates in arithmetic that underpin key results in mathematical logic, including Gödel’s incompleteness theorems and Löb’s theorem.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.