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: Hilbert-style deductive systems | Statement: [ZF, isFormalizedIn, Hilbert-style deductive systems]

Target entity: Hilbert-style deductive systems
Context triple: [ZF, isFormalizedIn, Hilbert-style deductive systems]

• A. Recherches sur la théorie de la démonstration
  Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
• B. New Foundations for Mathematical Logic
  New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
• 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. On a Problem of Formal Logic
  "On a Problem of Formal Logic" is a seminal philosophical and mathematical paper by F. P. Ramsey that contributed to the foundations of logic and helped inspire what is now known as Ramsey theory.
• E. Tarski’s theorem on the completeness of elementary algebra and geometry
  Tarski’s theorem on the completeness of elementary algebra and geometry is a foundational result in mathematical logic showing that the first-order theory of real closed fields (capturing elementary algebra and Euclidean geometry) is complete, decidable, and admits quantifier elimination.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Hilbert-style deductive systems
Triple: [ZF, isFormalizedIn, Hilbert-style deductive systems]

Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.

Target entity: Hilbert-style deductive systems
Target entity description: Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.

• A. Recherches sur la théorie de la démonstration
  Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
• B. New Foundations for Mathematical Logic
  New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
• 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. On a Problem of Formal Logic
  "On a Problem of Formal Logic" is a seminal philosophical and mathematical paper by F. P. Ramsey that contributed to the foundations of logic and helped inspire what is now known as Ramsey theory.
• E. Tarski’s theorem on the completeness of elementary algebra and geometry
  Tarski’s theorem on the completeness of elementary algebra and geometry is a foundational result in mathematical logic showing that the first-order theory of real closed fields (capturing elementary algebra and Euclidean geometry) is complete, decidable, and admits quantifier elimination.
• F. None of above. chosen

Target predicate: isFormalizedIn
Context triple: [ZF, isFormalizedIn, Hilbert-style deductive systems]

• A. isFormalizedBy
  Indicates that something is given a defined, structured, or official form through a specific method, process, or representation.
• B. formalizedUnder chosen
  Indicates that something has been officially established, defined, or codified within the framework, authority, or provisions of a particular formal system, agreement, or institution.
• C. formalizedAt
  Indicates the point in time or event at which something is officially established, documented, or given formal status.
• D. termFormalizedBy
  Indicates that a given term has been formally defined, specified, or codified by a particular formalization (such as a formal theory, document, or system).
• E. cessionFormalizedBy
  Indicates that a transfer or cession of rights, territory, or control is officially established, confirmed, or made legally binding by a specific formal act or instrument.
• F. None of above.