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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets

[sets as a well-founded hierarchy built from scratch]

14 ideas
The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD]
The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry]
There is no stage at which we can take all the sets to have been generated [Fine,K]
The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
Russell's paradox shows that there are classes which are not iterative sets [Shapiro]
It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro]
Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro]
The 'iterative' view says sets start with the empty set and build up [Brown,JR]
In the iterative conception of sets, they form a natural hierarchy [Swoyer]
Nowadays we derive our conception of collections from the dependence between them [Potter]
The iterative conception of set wasn't suggested until 1947 [Lavine]
The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]
The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine]