Timeline for What practical applications does set theory have?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2021 at 7:22 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
|
| May 8, 2017 at 22:30 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
edited body
|
| Dec 1, 2013 at 1:14 | comment | added | Andrej Bauer | Undecidability of halting problem has nothing to do with set theory, as it can be proved constructively in a weak system of arithmetic. | |
| Nov 30, 2013 at 23:21 | comment | added | Sasho Nikolov | @AndrejBauer I feel it may be a good idea to hint in the answer that "all possible" in fact means "essentially all that appear in practice". Plus the indecidability of the halting problem is another nice application of set theoretic arguments. | |
| Jan 2, 2010 at 16:56 | comment | added | Andrej Bauer | I was trying to be a bit informal in my answer, but yes, if we're precise then of course we hit the usual troubles with the Halting Problem. I just wanted to convey the fact that transfinite induction (up to $\epsilon_0$) suffices for all practical purposes. Nobody ever writes a program that tries to trick Peano arithmetic or ZFC or whatever formal system you like into not being able to decide termination. | |
| Jan 2, 2010 at 11:51 | comment | added | Neel Krishnaswami | All possible ways? I thought one way of understanding the incompleteness theorem was that there are always induction principles missing from any consistent theory. This is how I understand large cardinal axioms, so if I'm wrong I'd love to know why. | |
| Jan 2, 2010 at 0:58 | history | answered | Andrej Bauer | CC BY-SA 2.5 |