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: Peano arithmetic (under standard assumptions) | Statement: [Zermelo set theory, consistentRelativeTo, Peano arithmetic (under standard assumptions)]

Target entity: Peano arithmetic (under standard assumptions)
Context triple: [Zermelo set theory, consistentRelativeTo, Peano arithmetic (under standard assumptions)]

• 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. 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.
• 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. Gödel numbering
  Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: consistentRelativeTo
Context triple: [Zermelo set theory, consistentRelativeTo, Peano arithmetic (under standard assumptions)]

• A. consistentWith chosen
  Indicates that one entity does not contradict and is compatible or in agreement with another entity, condition, or set of constraints.
• B. relativePosition
  Indicates the spatial relationship of one entity’s location with respect to another entity’s position.
• C. possibleRelative
  Indicates a relationship where one entity may be related to another by family or kinship, but the exact nature of the relationship is uncertain or not fully established.
• D. relativeLength
  Indicates a comparative relationship between entities based on how long they are relative to one another.
• E. isComparedTo
  Indicates that one entity is evaluated or measured in relation to another to highlight similarities, differences, or relative qualities.
• F. None of above.