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: Post's theorem | Statement: [Rice's theorem, relatedTo, Post's theorem]

Target entity: Post's theorem
Context triple: [Rice's theorem, relatedTo, Post's theorem]

• A. Rice's theorem
  Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
• B. 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.
• 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. Tarski–Mostowski–Robinson theorem
  The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
• E. Kleene’s recursion theorem
  Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Post's theorem
Target entity description: Post's theorem is a fundamental result in computability theory that characterizes the arithmetical hierarchy by relating levels of definability to the Turing jump operation.

• A. Rice's theorem
  Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
• B. 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.
• 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. Tarski–Mostowski–Robinson theorem
  The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
• E. Kleene’s recursion theorem
  Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
• F. None of above. chosen