Timeline for Where in ordinary math do we need unbounded separation and replacement?
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| Jun 17, 2022 at 13:20 | comment | added | user21820 | But KP^P+AC proves these. So arguably only bounded specification and replacement are needed for them. No? | |
| Jul 22, 2021 at 2:12 | comment | added | David Roberts♦ | @arsmath it's been a long time, but yes, game theory is 'ordinary' mathematics (these days I would say "generic" instead, the term is less loaded). Game theory with payoff sets being arbitrary Borel sets of trees labelled by an arbitrary set? Less so, though I take my hat off to the people who get results in this area. If someone finds a use of nontrivial Borel determinacy for a non-Polish space in economics, they deserve more than a Nobel prize! | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Mar 6, 2013 at 9:22 | history | edited | Adam Epstein | CC BY-SA 3.0 |
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| Mar 5, 2013 at 10:47 | comment | added | arsmath | Game theory is not ordinary mathematics? Gale-Stewart games arose as an attempt to extend the determinacy of finite-length zero-sum games to infinite games. David Gale was a mathematical economist who's most famous for the Gale-Shapley stable matching algorithm that helped Shapley win the Nobel Prize in economics. Once determinacy of Gale-Stewart games for open and closed sets was shown, it's a natural question to wonder if it holds for sets higher in the Borel hierarchy. The theory of infinite games just turned out to be really, really hard. | |
| Mar 5, 2013 at 5:03 | comment | added | David Roberts♦ | +1 for the algebraic example, but I'm dubious that it counts as 'ordinary mathematics'. It certainly seems more ordinary than Borel determinacy, though. | |
| Mar 5, 2013 at 3:51 | history | edited | Adam Epstein | CC BY-SA 3.0 |
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| Mar 5, 2013 at 3:41 | history | edited | Adam Epstein | CC BY-SA 3.0 |
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| Mar 5, 2013 at 2:53 | history | edited | Adam Epstein | CC BY-SA 3.0 |
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| Mar 5, 2013 at 2:10 | history | answered | Adam Epstein | CC BY-SA 3.0 |