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Single Idea 18192

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII ]

Full Idea

For Boolos, the Replacement Axioms go beyond the iterative conception.

Gist of Idea

Do the Replacement Axioms exceed the iterative conception of sets?

Source

report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3

Book Ref

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.59

The 5 ideas with the same theme [axiom saying the bijection of any set is also a set]:

13028 Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
18192 Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
15899 Replacement was immediately accepted, despite having very few implications [Lavine]