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Single Idea 10779

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension ]

Full Idea

If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'.

Gist of Idea

A comprehension axiom is 'predicative' if the formula has no bound second-order variables

Source

Øystein Linnebo (Plural Quantification Exposed [2003], §1)

Book Ref

-: 'Nous' [-], p.73

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A Reaction

['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates]

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The 3 ideas with the same theme [axiom saying a set exists which satisfies a predicate]:

13031

Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]

13526

Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS]

10779

A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]