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Results tagged with axiom-of-choice
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user 497904
An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
6
votes
How much of the axiom of choice do you need in mathematics?
Each of the following is, at the very least, convenient for usual mathematics, but probably to a large extent unnecessary.
Countable/dependent choice. With them analysis and measure theory can be dev …
- 877
3
votes
0
answers
214
views
Basic cardinal arithmetic without choice
Do we know everything about addition and multiplication of cardinalities in choiceless set theory?
For example, let $M$ be a model of $\textsf{ZF}+\textsf{AD}+V=L(\mathbb{R})$, consider the sets $\mat …
- 877