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
Subscribe to:
Comments (Atom)
-
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... -
AC may be incorporated into the subset axiom. The subset axiom says that, assuming the use of "vacuous truth," any set X has a s...
-
This essay was recovered from a defunct web account. A discussion of Irreligion by John Allen Paulos. By PAUL CONANT Joh...