Combining Texts

Ideas for 'Structures and Structuralism in Phil of Maths', 'Alfred Tarski: life and logic' and 'Many, but almost one'

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6 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

10166

ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

10146

Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]

10147

The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]

10148

Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]

10149

Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]

10150

The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]