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: [ZF, isIncompletenessSubjectTo, Gödel incompleteness theorems]

Target entity: Gödel incompleteness theorems
Context triple: [ZF, isIncompletenessSubjectTo, 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. 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. 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. Remarks on the Foundations of Mathematics
  Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: isIncompletenessSubjectTo
Context triple: [ZF, isIncompletenessSubjectTo, Gödel incompleteness theorems]

• A. isSubjectTo
  Indicates that one entity is governed, affected, or constrained by the authority, rules, conditions, or influence of another entity.
• B. isComplete
  Indicates that an action, process, or object has finished all required steps or reached its final state with nothing remaining to be done.
• C. subjectToClosure
  Indicates that an entity is liable or scheduled to be closed, discontinued, or shut down under certain conditions or plans.
• D. decisionsSubjectTo
  Indicates that certain decisions are constrained by, dependent on, or must comply with specified conditions, approvals, or oversight.
• E. notClosedUnder
  Indicates that applying the operation or relation to elements of a set can produce results that do not belong to that set, so the set is not closed under that operation or relation.
• F. None of above. chosen