Are there interesting algebraic structures whose cardinality is greater than the continuum? Obviously, you could just build a product group of $\beth_2$ many groups of whole numbers to get to such a structure, but the properties of this group seem to be not very different from those you get when you just put together $\beth_1$ many whole number groups here.
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
2
|
|||||||
|
|
5
|
The MO question Martin is referring has several good examples of algebraic structures larger than the continuum; one that I did not see talked about there is Conway's field of surreal numbers. The surreal numbers form a proper class, so their cardinality dwarfs the cardinality of any set. |
||
|
|
You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.
|
2
|
This MO question "Cardinalities larger than the continuum in areas besides set theory" has recieved a couple of interesting answers, also algebraic ones (e.g. Zariski cotangent space of a manifold which is not smooth, automorphism tower length of a group) |
||
|
|
