Combining Texts
Ideas for
'Parmenides', 'Introduction to Zermelo's 1930 paper' and 'Plurals and Complexes'
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6 ideas
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17833
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The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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17834
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Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10676
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The Axiom of Choice is a non-logical principle of set-theory [Hossack]
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10686
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The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17837
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Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10687
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Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
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