Combining Texts
Ideas for
'Philosophical Explanations', 'Naturalism in Mathematics' and 'Introducing the Philosophy of Mathematics'
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10 ideas
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
18194
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'Forcing' can produce new models of ZFC from old models [Maddy]
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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
18195
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A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
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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 / f. Axiom of Infinity V
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Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
18193
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The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18169
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Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
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