Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'Bertrand Russell: Spirit of Solitude' and 'Understanding the Infinite'

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15 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
15945 Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
15914 An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
15921 Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
15937 Those who reject infinite collections also want to reject the Axiom of Choice [Lavine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
15936 The Power Set is just the collection of functions from one collection to another [Lavine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
15899 Replacement was immediately accepted, despite having very few implications [Lavine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
15930 Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
15920 Pure collections of things obey Choice, but collections defined by a rule may not [Lavine]
15898 The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
15919 The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
15900 The iterative conception of set wasn't suggested until 1947 [Lavine]
15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]
15932 The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15933 Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
15913 A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine]