What other axioms in set theory are stronger than AC ? I mean what are those axioms that will imply AC ?



What axioms are stronger than the Axiom of choice?
The axiom "every set is constructible" (denoted **V** = **L**), and the axiom "every set is definable from an ordinal parameter" (denoted often as **V**= **HOD**, and sometimes as **V**= **OD**) each implies AC, and each is provably stronger than AC.



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> > More specifically, it is well-known that:
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> > **(a)** (Within ZF), **V** = **L** implies **V** = **HOD**, and **V** = **HOD** implies AC.
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> > **(b)** Neither of the above implications is reversible.
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**Historical Note:** The axiom **V** = **L** was introduced by Gödel in his seminal work on the consistency of AC and GCH with ZF. The axiom **V**= **HOD** was first publicly introduced in a joint paper of Myhill and Scott, but their paper acknowledges that the axiom was independently considered by a number of people, including Gödel, Post, and the joint work of Vopěnka and Balcar.


