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: second-order Peano arithmetic | Statement: [Peano arithmetic, hasVariant, second-order Peano arithmetic]

Target entity: second-order Peano arithmetic
Context triple: [Peano arithmetic, hasVariant, second-order Peano arithmetic]

• A. Peano arithmetic
  Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number theory.
• B. Skolem arithmetic
  Skolem arithmetic is a fragment of first-order arithmetic focusing on the natural numbers with multiplication but without addition, studied for its distinctive decidability and model-theoretic properties.
• C. Lectures on the Logic of Arithmetic
  Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
• D. Gentzen’s consistency proof for arithmetic
  Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
• E. arithmetization of syntax
  Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
• 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: second-order Peano arithmetic
Triple: [Peano arithmetic, hasVariant, second-order Peano arithmetic]

Second-order Peano arithmetic is a formal axiomatic system for the natural numbers that uses second-order logic to characterize them categorically up to isomorphism.

Target entity: second-order Peano arithmetic
Target entity description: Second-order Peano arithmetic is a formal axiomatic system for the natural numbers that uses second-order logic to characterize them categorically up to isomorphism.

• A. Peano arithmetic chosen
  Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number theory.
• B. Skolem arithmetic
  Skolem arithmetic is a fragment of first-order arithmetic focusing on the natural numbers with multiplication but without addition, studied for its distinctive decidability and model-theoretic properties.
• C. Lectures on the Logic of Arithmetic
  Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
• D. Gentzen’s consistency proof for arithmetic
  Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
• E. arithmetization of syntax
  Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
• F. None of above.