It's not the axiom of choice, but Gödel's constructible universe was introduced to demonstrate the consistency of this statement, which was shown to be independent of Zermelo–Fraenkel set theory by Paul Cohen using the technique of forcing, for which he won a 1966 Fields Medal.
Chris Freiling argued that this statement is false because it is equivalent to the negation of his axiom of symmetry. It's not the axiom of choice, but Gödel's constructible universe was introduced to demonstrate the consistency of this statement, which was shown to be independent of Zermelo–Fraenkel set theory by Paul Cohen using the technique of forcing, for which he won a 1966 Fields Medal. A reformulation of this statement says that the first beth number is equal to the first aleph number, or alternatively, that the number of reals is aleph-one. For 10 points, identify this assertion in set theory that states that there are no sets whose cardinality is strictly between that of the integers and that of the real numbers.
Chris Freiling argued that this statement is false because it is equivalent to the negation of his axiom of symmetry.
continuum hypothesis [or CH] &lt;Thompson&gt;