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Single Idea 18107

[filed under theme 4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set ]

Full Idea

A 'proper class' cannot be a member of anything, neither of a set nor of another proper class.

Gist of Idea

A 'proper class' cannot be a member of anything

Source

David Bostock (Philosophy of Mathematics [2009], 5.4)

Book Ref

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.151

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The 4 ideas with the same theme [general ways of categorising types of set]:

18958

In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]

18107

A 'proper class' cannot be a member of anything [Bostock]

13651

A set is 'transitive' if contains every member of each of its members [Shapiro]

15921

Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine]