Combining Texts
Ideas for
'works', 'Introduction to Mathematical Logic' and 'Set Theory and Its Philosophy'
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8 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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Usually the only reason given for accepting the empty set is convenience [Potter]
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The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
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The empty set avoids having to take special precautions in case members vanish [Walicki]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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Infinity: There is at least one limit level [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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Nowadays we derive our conception of collections from the dependence between them [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
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4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
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Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
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