Discussion
In ZFC, the axiom of global choice cannot be stated as such because it involves existential quantification on classes: so it is not a statement of the language of ZFC (nor even an infinite number of statements like axiom schemes requiring universal quantification on classes). It can, however, be stated for a given explicit class, e.g., one can state the fact that such-or-such an explicit class-function is a choice function for V \ { ∅ } or that such-or-such a class-relation is a well-ordering of V: in this form (i.e., for some explicit class function that is tedious but possible to write down), the axiom of global choice follows from the axiom of constructibility.
In Gödel-Bernays, global choice does not add any consequence about sets beyond what could have been deduced from the ordinary axiom of choice.
Global choice is a consequence of the axiom of limitation of size.
Read more about this topic: Axiom Of Global Choice
Famous quotes containing the word discussion:
“Americans, unhappily, have the most remarkable ability to alchemize all bitter truths into an innocuous but piquant confection and to transform their moral contradictions, or public discussion of such contradictions, into a proud decoration, such as are given for heroism on the battle field.”
—James Baldwin (1924–1987)
“We cannot set aside an hour for discussion with our children and hope that it will be a time of deep encounter. The special moments of intimacy are more likely to happen while baking a cake together, or playing hide and seek, or just sitting in the waiting room of the orthodontist.”
—Neil Kurshan (20th century)
“My companion and I, having a minute’s discussion on some point of ancient history, were amused by the attitude which the Indian, who could not tell what we were talking about, assumed. He constituted himself umpire, and, judging by our air and gesture, he very seriously remarked from time to time, “you beat,” or “he beat.””
—Henry David Thoreau (1817–1862)