structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

[axiom saying the bijection of any set is also a set]

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