Combining Texts
Ideas for
'Demonstratives', 'Introducing the Philosophy of Mathematics' and 'On boundary numbers and domains of sets'
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7 ideas
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
8665
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A 'proper subset' of A contains only members of A, but not all of them [Friend]
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8672
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A 'powerset' is all the subsets of a set [Friend]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
8677
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Set theory makes a minimum ontological claim, that the empty set exists [Friend]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
8666
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Infinite sets correspond one-to-one with a subset [Friend]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17832
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Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
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8682
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Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13028
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Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
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