Combining Philosophers
Ideas for Archimedes, Michal Walicki and Feferman / Feferman
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8 ideas
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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17752
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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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17753
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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 / j. Axiom of Choice IX
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10146
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Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
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10147
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The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
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10148
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Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
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10149
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Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
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10150
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The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
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4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
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17759
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Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
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