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4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set

[general ways of categorising types of set]

4 ideas
In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
A 'proper class' cannot be a member of anything [Bostock]
A set is 'transitive' if contains every member of each of its members [Shapiro]
Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine]