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: Lindenbaum lemma | Statement: [Henkin construction, relatedTo, Lindenbaum lemma]

Target entity: Lindenbaum lemma
Context triple: [Henkin construction, relatedTo, Lindenbaum lemma]

• A. König's lemma
  König's lemma is a fundamental result in graph theory and logic stating that every finitely branching infinite tree has an infinite path.
• B. Ultrafilter lemma
  The ultrafilter lemma is a set-theoretic principle weaker than the full Axiom of Choice that guarantees every filter can be extended to an ultrafilter and underlies several key results in topology and analysis.
• C. Bailey lemma
  The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
• 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. Łoś–Tarski preservation theorem
  The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Lindenbaum lemma
Target entity description: The Lindenbaum lemma is a result in mathematical logic stating that any consistent set of formulas in a formal language can be extended to a maximally consistent (complete) theory.

• A. König's lemma
  König's lemma is a fundamental result in graph theory and logic stating that every finitely branching infinite tree has an infinite path.
• B. Ultrafilter lemma chosen
  The ultrafilter lemma is a set-theoretic principle weaker than the full Axiom of Choice that guarantees every filter can be extended to an ultrafilter and underlies several key results in topology and analysis.
• C. Bailey lemma
  The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
• 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. Łoś–Tarski preservation theorem
  The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
• F. None of above.