Combining Texts
Ideas for
'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'A Tour through Mathematical Logic'
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5 ideas
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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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 / e. Axiom of the Empty Set IV
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13529
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Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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13526
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Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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17837
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Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
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