AC may be incorporated into the subset axiom.
The subset axiom says that, assuming the use of "vacuous truth," any set X has a subset.
AC would say that every pure set except those of cardinality less than 2 (as in {0,1}) has a nonempty proper subset.
But such a formulation requires an axiom of foundation, or the equivalent, in order to outlaw sets of "cardinality" less than 0. (That is, to forbid infinite descent definitions of not-so-primitive elements.)
Monday, January 10, 2022
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I have read in a few places that C.S. Peirce was the first to introduce quantifiers into logic. Hence, I draw attention to the words of Aug...
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When you see X ⊃ Y, you are to read "X implies Y" or "If X, then Y." Sometimes you may see the modern form, X —> Y, i...
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When you see X ⊃ Y, you are to read "X implies Y" or "If X, then Y." Sometimes you may see the modern form, X —> Y, i...